what are the divisibility rules for 3 and 9

The divisibility rules for 3 and 9 are quite similar. As defined above, if the sum of the digits of a number is a multiple of 3 or divisible by 3, then the number is divisible by 3. Similarly, if the sum of the digits of a number is a multiple of 9 or divisible by 9, then the number is divisible by 9.

Full Answer

What numbers are divisible by 3 and 9?

Every number divisible by 9 is divisible by 3. For example, 7425 is divisible by 9, hence it is divisible by 3. However, a number divisible by 3 is not necessarily divisible by 9. For example 6, 12, 15, 21, 24, 30 are all divisible by 3 but none of them is divisible by 9. The rule for divisibility by 3 can be easily obtained following the same ...

Are all multiples of 9 divisible by 3?

Yes, since 9 is divisible by 3, any multiple of 9 is also divisible by 3. A multiple of 9, divided by 3, equals the number that is multiplied by 9, times 3. For example, 8 • 9=72. 72/3=24. 8 • 3=24

Is 994 divisible by 3?

To find out if 994 is divisible by 3, we will add up the digits that make 994 as follows: 9 + 9 + 4 = 22 We know that if the sum of the numbers that make up 994 is divisible by 3, then 994 is divisible by 3. Since the sum of the digits in 994 is not divisible by 3, 994 is also NOT divisible by 3.

Is 94 divisible by 3?

Since the sum of the digits in 94 is not divisible by 3, 94 is also NOT divisible by 3. Thus, the answer to the question "Is 94 divisible by 3?" is as follows: Note: If you divide 94 by 3, you get 31.33 which is not a whole number.

What is the divisibility rule for 3?

Divisibility rule for 3 states that a number is completely divisible by 3 if the sum of its digits is divisible by 3. Consider a number, 308. To check whether 308 is divisible by 3 or not, take sum of the digits (i.e. 3+0+8= 11).

What is the rule of divisibility of 9?

Divisibility rules for numbers 1–30DivisorDivisibility condition8The last three digits are divisible by 8.Add four times the hundreds digit to twice the tens digit to the ones digit. The result must be divisible by 8.9Sum the digits. The result must be divisible by 9.10The ones digit is 0.67 more rows

Why does divisibility rule for 3 and 9 work?

Because 10=9+1, 100=99+1, 1000=999+1 and so on, we can see that every power of 10 is just 1 more than a multiple of 9, and so this method for divisibility by 3 works for 9 too.

Which of the following is divisible by 3 not 9?

Hence, the numbers 21, 24, 30, 33 and 39 are divisible by 3 not by 9.

What is the rule of 9 in maths?

The divisibility test that an integer is divisible by 9 iff the sum of its digits is divisible by 9.

Is 3 divisible by 9 yes or no?

If the sum of the digits is not divisible by 9, then 3 is not divisible by 9. 3 is not divisible by 9, Therefore, 3 is not divisible by 9 and the answer to the question, "Is 3 Divisible By 9?" is No.

Why does the 9 divisibility rule work?

0:028:03Divisibility by 3 and by 9: Why do they work? (TANTON Mathematics)YouTubeStart of suggested clipEnd of suggested clip5 plus 2 is 7 7 is 14 17 21 24 24 is a multiple 3 and parry that means this guy is divisible by 3 inMore5 plus 2 is 7 7 is 14 17 21 24 24 is a multiple 3 and parry that means this guy is divisible by 3 in fact the same rule actually holds for 9 divisible by 9 add up the digits.

What is the rule for multiples of 9?

Consider the multiples of 9: 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, ....... In each case it can be observed that the sum of the digits is divisible by 9. A number is divisible by 9, if the sum is a multiple of 9 or if the sum of its digits is divisible by 9.

Divisibility by 3

The three-digit divisibility rule asserts that if the sum of a whole number's digits is a multiple of three, the original number is also divisible by three. It is simple to determine if a smaller number is divisible by 3 or not using the 3 multiplication table or skip counting by 3.

Divisibility by 9

The divisibility rule of 9 asserts that if a number's sum of digits is divisible by 9, the number is divisible by 9 as well. It assists us with a variety of topics like divisors, HCF, LCM, measures, and division. Divisibility by 9 is a rule that allows us to determine whether or not an integer is divisible by 9 without having to do long division.

Divisibility Rule of 3 and 9

The three-digit divisibility rule and the nine-digit divisibility rule are quite similar. As previously stated, the divisibility rule for the divisibility test of 3 asserts that if a number's sum of all digits is divisible by 3, the number is also divisible by 3.

Points to Remember

A divisibility rule is a simple method for determining whether or not an integer is divisible by a fixed divisor without having to divide it, usually by looking at its digits

Sample Questions

Ans: Take the digits of the number 111 and add them together. 1 + 1 + 1 equals 3. Because the total of the digits is divisible by three, the number 111 is divisible by three as well.

What is the Divisibility Rule for 3.?

Divisibility Rule for 3. If the sum of the digits of a number is divisible by 3, then the number is divisible by 3. Some examples of numbers divisible by 3 are as follows. The number 85203 is divisible by 3 because the sum of its digits 8 + 5 + 2 + 0 + 3 = 18 is divisible by 3.

Why is 79154 not divisible by 3?

The number 79154 is not divisible by 3 because the sum of its digits 7 + 9 + 1 + 5 + 4 = 26 is not divisible by 3. If the sum of the digits of a number is divisible by 9, then the number is divisible by 9. Some examples of numbers divisible by 9 are as follows.

Is 51984 divisible by 9?

The number 51984 is divisible by 9 because the sum of its digits 5 + 1 + 9 + 8 + 4 = 27 is divisible by 9. The number 91403 is not divisible by 9 because the sum of its digits 9 + 1 + 4 + 0 + 3 = 17 is not divisible by 9. Problem. Find the divisibility of the numbers in following table. Solution.

What is the rule for 3?

The Rule for 3: A number is divisible by 3 if the sum of the digits is divisible by 3.

How to find if a number is even?

Step 1: Determine if the number is even. It ends in 8, so this number is even. Therefore it is divisible by 2. Step 2: Add the digits together. 2 + 3 + 9 + 0 + 8 = 22.

What is the rule for 154,608.?

Example:154,608. Step 1: This number is even and is therefore divisible by 2. Step 2: 1 + 5 + 4 + 6 + 0 + 8 =24. Step 3: 24 is divisible by 3 because 3 x 8 = 24. Step 4: Because the number is divisible by 2 and 3, it is also divisible by 6. The Rule for 9: The prime factors of 9 are 3 and 3.

How to tell if a number is prime or not?

This will help you to also determine if a number is prime or not. When a number is divisible by something other than 1 or itself, it is not prime. So, if we can show that 3, 6 or 9 go into the number, we know that the number is not prime without doing any long division.

What is the prime factor of 9?

The Rule for 9: The prime factors of 9 are 3 and 3. So we can use a very similar rule to determine if a number is divisible by 9. Basically, we will see if the sum of the digits is divisible by 9. If it is, then the actual number is also divisible by 9. This is done the same way we checked the rule for 3.

How to find 34,911?

Example: 34,911. Step 1: Add up the digits. 3 + 4 + 9 + 1 + 1 = 18. Step 2: Determine if 3 divides evenly into the sum of 18. Yes, 3 x 6 = 18. So 3 goes evenly into 18. Step 3: Use the result to determine if 3 goes into 34,911. Because 3 divides into 18 evenly, 3 also divides evenly into 34,911.

What are the rules for divisibility?

However, some of the rules are easier to use than others. For the rest, it might just be simpler to actually divide. Here is a look at the rules for 3, 6, and 9.

What is the remainder of 1236?

For example, 1236 is divisible by 3 as the sum of all digits that is 1+2+3+6 = 12. We know that 12 is divisible by 3. Now, 1236 is divisible by 4 as the number formed by the last two digits, that is, 36 is divisible by 4. Therefore, 1236 ÷ 4 = 309 is the quotient and the remainder is 0.

How to tell if a whole number is divisible by 3?

A whole number is said to be divisible by 3 if the sum of all the digits of a whole number is exactly divided by 3; this rule is referred to as the divisibility rule of 3. Without doing division we can find out whether a number is divisible by 3 or not. For example, 45 is divisible by 3 as the sum of 45 is (4+5) = 9, is divided by 3. Hence, 45 is said to be divisible by 3, because it gives the quotient as 15 and the remainder as 0.

What is the sum of 1377?

a) In 1377, the sum of all the digits = 1+3+7+7 = 18. Since 18 is divisible by 3, it means 1377 is also divisible by 3. Here, 1377 ÷ 3 = 459 is the quotient and the remainder is 0.

How are the divisibility tests of 3 and 4 different?

The divisibility test of 3 states that the number is divisible by 3 if the sum of all digits of a number is divisible by 3 , whereas, the divisibility test of 4 states that the number is said to be divisible by 4 if the number formed by the last two digits , that is , the digit at tens place and ones place is divisible by 4.

What is the divisibility rule of 3?

The divisibility rule of 3 states that if the sum of the digits of a whole number is a multiple of 3, then the original number is also divisible by 3. With the help of the multiplication table of 3 or by using skip counting by 3 (starting at 0 and adding 3) it is easy to find that a smaller number is divisible by 3 or not. But for larger numbers, we can check if that number is completely divisible by 3 or not without doing the actual division.

Is 52884 a quotient?

For example, 52884 is divisible by 3 as the sum of all digits that is 5+2+8+8+4 = 27 is divisible by 3. Here, 52884 ÷ 3 = 17628 is the quotient and the remainder is 0. Note that the sum of the digits of the number 27 is 2 + 7 = 9 is also divisible by 3. We can repeat this process so that we get the sum closer to 3 and find out whether the number is divisible by 3 or not.

Is the divisibility rule of 3 the same as the divisibility rule of 9?

The divisibility rule of 3 and the divisibility rule of 9 are slightly similar. As we already discussed above that the divisibility rule or divisibility test of 3 states that if the sum of all digits of a number is divisible by 3 then the number is also divisible by 3. Just like the divisibility rule of 3, the divisibility rule of 9 states that the number is said to be divisible by 9 if the sum of all the digits of a number is divisible by 9.

What is the Divisibility Rule of 9?

The divisibility rule of 9 helps us to find whether a number is a multiple of 9 or not without performing the actual division. Some of the multiples of 9 are 9, 18, 27, 36, 45, etc. Do you see a common pattern in the sum of the digits of these numbers? The sum of digits of all these numbers is itself a multiple of 9. For example, 18 is 1+8 = 9, which is divisible by 9, 27 is 2+7 = 9, which is divisible by 9, etc. So, as per the divisibility test of 9, if the sum of all the digits of a number is a multiple of 9, then the number is also divisible by 9.

What is the sum of all the digits of 1450?

The sum of all the digits of 1450 is 1+4+5+0 = 10, which is not divisible by 9. So, 1450 is not divisible by 9, as per the divisibility test for 9.

How to tell if a number is divisible by 3?

To check if a number is divisible by 3 or not, the sum of all the digits of the number should be divisible by 3, while on the other hand in the case of divisibility rule by 9, if the sum of all the digits of the number is divisible by 9, then the number is also a multiple of 9. For example, to find whether 459072 is divisible by 9 and 3 or not, ...

How to find the divisibility of 9?

Let us look at the steps to apply the divisibility rule of 9 easily with any large or smaller numbers: Step 1: Find the sum of all the digits of the given number. Step 2: Check if the sum is divisible by 9 or not . If it is still a large number, add the digits again.

What happens if the final sum is divisible by 9?

Step 4: If the final sum is divisible by 9, then the original number would also be divisible by 9.

What is the smallest number of 3 digits?

Solution: The smallest 3-digit number is 100. But to check which smallest number of 3 digits can be a multiple of 9, we have to find the sum of the digits. Let us consider units place as blank, so we have 10_. Now we have to find a digit that could come in the blank such that the sum of 1 and that digit is 9. That digit is 8, as 1+8=9. Therefore, 108 is the smallest 3-digit number which is divisible by 9.

Is 13 divisible by 9?

Here, 13 is not divisible by 9, so as per the divisibility test by 9, we can say that 724 is also not divisible by 9.

What is the divisibility test for 8?

The divisibility test for 8 is applied in the case of numbers with at least three digits. A number is divisible by 8 if the three digit number formed by the digits in ones, tens and the hundreds spots is divisible by 8. In the number 5864, we see that the number formed by the digits in ones, tens and hundreds spot is 864, which is divisible by 8, so the number is divisible by 8.

What is the divisible by 2?

On the off chance that the ones digit or unit's place digit of a number is either 0, 2, 4, 6 or 8 then the number is said to be divisible by 2. In different terms, on the off chance that the last digit of the number is even, at that point it is constantly divisible by 2. For instance, how about we take 24. The last digit is even. 4 is divisible by 2, hence the number 24 is divisible by 2.

What is the sum of the digits in 123?

123: Here the sum of the digits is 6 and 6 is divisible by 3. So the number 123 is divisible by 3.

What is the procedure of whether a given number is exactly divisible by another number without really working out the process of?

The procedure of whether the given number is exactly divisible by another number without really working out the process of division is known as the test of divisibility. Being exactly divisible implies that on division there is no leftover portion left. For understanding the divisibility rules for any number we have to know its divisibility with numbers like 2, 3, 4, 5, 9, 10 and 11.

What is the number that is not divisible by 22?

Solution: For a number to be divisible by 22, it must be divisible both by 2 and 11. Since A and C are odd numbers, they are not divisible by 22. In the case of D, (5 + 8) - (6 + 2) = 13 - 8 = 5, which is not a multiple of 11, so D is not divisible by 11, hence it is not divisible by 22.

How to do long division?

A Few Tips for Long Division: 1 Write down a different table for the divisor before you begin the problem. For instance, if the divisor is 11 you record 11, 22, 33, 44, 55, 66, 77, 88, 99, and so forth. This can help you in avoiding mistakes. 2 Put a 0 in the left places of the remainder that you aren't utilizing. Ensure you keep every one of your numbers arranged. Composing perfectly and keeping the numbers arranged can truly help you with making fewer mistakes. 3 Double check the problem with verification. When you have your answer, do the problem backwards by multiplication to check whether your solution is correct or not. 4 The following are a couple of more instances of long division. Endeavor to work through these problems yourself to check whether you get similar outcomes.

What is 11 underneath 18?

Next, we compose 11 underneath the 18 in light of the fact that 1 × 11 = 11. At that point, we subtract 11 from 18. This equals 7, which we record.

Divisibility by 3

• [Click Here for Sample Questions] The three-digit divisibility rule asserts that if the sum of a whole number's digits is a multiple of three, the original number is also divisible by three. It is simple to determine if a smaller number is divisible by 3 or not using the 3 multiplication table or skip counting by 3. However, we may check whether a ...

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Divisibility by 9

Divisibility Rule of 3 and 9

Points to Remember