Divisibility rule
A divisibility rule is a shorthand way of determining whether a given number is divisible by a fixed divisor without performing the division, usually by examining its digits. Although there are divisibility tests for numbers in any radix, or base, and they are all different, this article presents rules and examples only for decimal, or base 10, numbers.
What are the divisibility rules from 1 to 10?
MatchRule for 1. If the number is a number.Rule for 2. If the digit ends in 0, 2, 4, 6, or 8.Rule for 3. If the sum of the digits in the number is divisible by 3.Rule for 4. If the last two digits of the number is divisible by 4.Rule for 5. If the number ends in 0 or 5.Rule for 6. ... Rule for 7. ... Rule for 8.More items...
What is the divisibility rule of 10 and 11?
80, 210, 790, 9990, 1000, 2658970 are divisible by 10 because all numbers ends in 0. Divisibility by 11. A number is divisible by 11 if the sum of the digits in the odd places and the sum of the digits in the even places difference is a multiple of 11 or zero. 11 is divisible by 11.
What is the divisibility rule of 5 and 10?
Divisibility Rule of 5 and 10 The last digit in the given number is 0, hence, 73540 is divisible by 5. The same condition is satisfied for the divisibility rule of 10 since the last digit is zero. Therefore, 73540 is divisible by 5 as well as 10. Let us take another example of the number 10105.
What is the divisibility rule of 2 5 and 10?
To check if a number is divisible by 2, 5 and 10, look at its final digit. A number is divisible by 2 if it ends in 2, 4, 6, 8 or 0. A number is divisible by 5 if it ends in 5 or 0. A number is divisible by 10 if it ends in a 0.
What is the divisibility of 15?
According to the divisibility rule of 15, a numeral is divisible by 15 if it is divisible by both 3 and 5. Since the unit digit of 1440 is 0, it is divisible by 5. Hence, the sum of digits is 9, it is divisible by 3. Since 1440 is divisible by both 3 and 5, 1440 is divisible by 15.
What is the divisible by 12?
Divisibility guidelines for 12: If it is divisible by both 3 and 4, then the number is divisible by 12.
Is 10 divisible by 5 yes or no?
The number 10 is divisible by 5. Every number with 0 as a last digit is also divisible by 5, because we can represent it as a sum of tens. As for a number with a different last digit, we can always represent it as a sum of a number with 0 as a last digit and the number of ones.
What is the divisibility of 11?
What is the Divisibility Rule of 11? The divisibility by 11 rule states that if the difference between the sum of the digits at odd places and the sum of the digits at even places of the number, is 0 or divisible by 11, then the given number is also divisible by 11.
What is the divisible Rule of 7?
What is the Divisibility Rule of 7? The divisibility rule of 7 states that, if a number is divisible by 7, then “the difference between twice the unit digit of the given number and the remaining part of the given number should be a multiple of 7 or it should be equal to 0”. For example, 798 is divisible by 7.
What is the divisibility rule of 2 to 11?
Divisibility Tests For 2, 3, 5, 7 And 11 Divisibility Test for 2: The last digit is 0, 2, 4, 6, or 8. Divisibility Test for 3: The sum of the digits is divisible by 3. Divisibility Test for 5: The last digit is 0 or 5. Divisibility Test for 7: Cross off last digit, double it and subtract.
What are divisibility of 5?
Divisibility by 5 is easily determined by checking the last digit in the number (475), and seeing if it is either 0 or 5. If the last number is either 0 or 5, the entire number is divisible by 5. If the last digit in the number is 0, then the result will be the remaining digits multiplied by 2.
What are the divisibility rules for 2 3 5 and 10?
A number is divisible by 2 if it ends in 0, 2, 4, 6 or 8. This means that it is even. 3044 is therefore not divisible by 3, because 11 is not divisible by 3. A number is divisible by 5 if it ends in 0 or 5.
What is the divisibility rule of 11?
Divisibility Rules for 11 If the difference of the sum of alternative digits of a number is divisible by 11, then that number is divisible by 11 completely.
What is the divisibility of 11?
What is the Divisibility Rule of 11? The divisibility by 11 rule states that if the difference between the sum of the digits at odd places and the sum of the digits at even places of the number, is 0 or divisible by 11, then the given number is also divisible by 11.
Which number is divisibility by 11?
Here an easy way to test for divisibility by 11. Take the alternating sum of the digits in the number, read from left to right. If that is divisible by 11, so is the original number. So, for instance, 2728 has alternating sum of digits 2 – 7 + 2 – 8 = -11.
Which is exactly divisible by 11?
Consider the following numbers which are divisible by 11, using the test of divisibility by 11: (i) 154, (ii) 814, (iii) 957, (iv) 1023, (v) 1122, (vi) 1749, (vii) 53856, (viii) 592845, (ix) 5048593, (x) 98521258. -1 is divisible by 11.
What is meant by divisibility rules?
A divisibility test is an easy way to identify whether the given number is divided by a fixed divisor without actually performing the division proc...
What is the divisibility rule for 2 and 5?
Divisibility rule for 2: The last/unit digit of the given number should be an even number or the multiples of 2. (i.e.,) 0, 2, 4, 6, and 8. Divisi...
What is the divisibility rule for 7 and give an example?
The difference between twice the unit digit of the given number and the remaining part of the given number should be a multiple of 7 or it should b...
Write down the divisibility rule for 9.
The sum of the digits of the given number should be divisible by 9. For example, 2979 is divisible by 9. (i.e.,) 2+9+7+9 = 27, which is divisible b...
What is the divisibility rule for 13?
The sum/addition of four times of the unit digit and the remaining part of the given number should be a multiple of 13. For example, 1092 is divisi...
What is the divisibility rule for 2 and 5?
Divisibility rule for 2: The last/unit digit of the given number should be an even number or the multiples of 2. (i.e.,) 0, 2, 4, 6, and 8.
What is the divisibility rule for 7 and give an example?
The difference between twice the unit digit of the given number and the remaining part of the given number should be a multiple of 7 or it should be zero. For example, 147 is divisible by 7. Here, the unit digit is 7. When it is multiplied by 2, we get 14, and the remaining part is 14. Therefore, the difference between 14 and 14 is 0.
What is the divisible number of a number that is even?
If a number is even or a number whose last digit is an even number i.e. 2,4,6,8 including 0, it is always completely divisible by 2.
How to divisible a number by 11?
Subtract the last digit of the number from the rest of the number. If the resultant value is a multiple of 11, then the original number will be divisible by 11.
What is the purpose of divisibility tests?
As the name suggests, divisibility tests or division rules in Maths help one to check whether a number is divisible by another number without the actual method of division. If a number is completely divisible by another number then the quotient will be a whole number and the remainder will be zero. Since every number is not completely divisible by ...
What is the number divisible by 2 and 3?
Numbers which are divisible by both 2 and 3 are divisible by 6. That is, if the last digit of the given number is even and the sum of its digits is a multiple of 3, then the given number is also a multiple of 6.
How to tell if 308 is divisible by 3?
To check whether 308 is divisible by 3 or not, take sum of the digits (i.e. 3+0+8= 11). Now check whether the sum is divisible by 3 or not. If the sum is a multiple of 3, then the original number is also divisible by 3. Here, since 11 is not divisible by 3, 308 is also not divisible by 3.
What is the divisibility rule of 19?
Divisibility Rule of 19 - If we get 0 as the remainder when dividing a number by 19, then that number is considered divisible by 19. According to the divisibility rule of 19, first, we have to multiply the ones place digit by 2. Then, we add the product to the rest of the number to its left (excluding the digit at the units place). If that sum results in a number divisible by 19, then the original number is also divisible by 19.
How to find the divisibility of 7?
Look at the steps given below to apply the divisibility test of 7: Step 1: Identify the ones place digit of the number and multiply it by 2. Step 2: Find the difference between the number obtained in step 1 and the rest of the number. Step 3: If the difference is divisible by 7, then the number is divisible by 7.
How to divisible by 17?
Divisibility Rule of 17 - A number is divisible by 17 when 17 divides it completely without leaving any non-zero remainder. According to the divisibility rule of 17, first, we have to multiply the ones place digit by 5. Then, we subtract the product from the rest of the number to its left (excluding the digit at the units place). If that difference results in a number divisible by 17, then the original number is also divisible by 17.
What is the purpose of the divisibility test?
Divisibility rules in math are a set of specific rules that apply to a number to check whether the given number is divisible by a particular number or not. Some known divisibility tests are for numbers 2 to 20. It helps us to find the factors and multiples of numbers without performing long division. A person can mentally check whether ...
How to tell if a number is divisible by a divisor?
A divisibility rule is a kind of shortcut that helps us to identify if a given integer is divisible by a divisor by examining its digits, without performing the whole division process. Multiple divisibility rules can be applied to the same number which can quickly determine its prime factorization. A divisor of a number is an integer that completely divides the number without leaving any remainder.
What are the intermediate divisibility rules?
Intermediate divisibility rules are applied to prime numbers which are less than 20 and greater than 10. Divisibility tests for prime numbers 2, 3, 5, 7, and 11 are already discussed above. Here, let's learn about the divisibility rules of 13, 17, and 19.
What is an even number?
A number is even or a number whose last digit is an even number i.e. 0, 2, 4, 6, and 8.
What is the Divisibility Rule for 8.?
In a number, if the last three digits are zeros or the number formed by the last 3 digits is divisible by 8, then the number is divisible by 8.
What is the difference between two digits in one's place and the number formed by other digits?
In a number, if the difference between twice the digit in one's place and the number formed by other digits is either zero or a multiple of 7, then the number is divisible by 7.
What is the sum of the digits in the given number 252?
The sum of the digits in the given number 252 is 9 which is a multiple of 3.
What happens when a number ends with 0?
If a number ends with 0, then it is divisible by 10.
What is the divisible number of even numbers?
We already know that all even numbers are divisible by 2.
What is it called when a number ends with one of the following digits?
A number ends with one of the following digits is called as even number.
Is 5832 a divisible number?
Solution : The given number 5832 ends with 2. So, it is even number and divisible by 2. Check whether the number 5832 is divisible by 3. Add all the digits. 5 + 8 + 3 + 2 = 18. The sum of the digits in the given number 5832 is 18 which is a multiple of 3. Therefore, the given number 5832 is divisible by both 2 and 3.
What is the divisibility of a number with 4 or more digits?
A number with 4 or more digits is divisible by 8, if the number formed by the last three digits is divisible by 8. Example 1000, 2104, 1416, the last 3 digits are 000, 104, 416 and all these are divisible by 8. Quick Note: The divisibility for numbers with 1, 2 or 3 digits by 8 has to be checked by actual division.
What is a number with 3 or more digits divisible by 4?
A number with 3 or more digits is divisible by 4 if the number formed by its last two digits (i.e. ones and tens) is divisible by 4. Example 4612, here we will take the last 2 digits i.e. 12 and we all know that 12 is divisible by 4 therefore 4612 is also divisible by 4.
How to check if a number is divisible by 7?
To check the divisibility by 7 you must first double the last digit and subtract it from a number made by the other digits. If the resulting number is divisible by 7 then the rule is valid. Example 343, following the rule double the last digit = 6 subtracting it from 34 – 6 = 28 and we know that 7 x 4 = 28. Hence the rule follows.
What is the purpose of the Divisibility Rules?
Divisibility Rules are a set of rules which one can use while dividing numbers or to check if a particular number is divisible by another number or not. For example, in order to check if 729 is divisible by 9 or not, you can use the divisibility test of 9.
What are the rules for divisibility?
Divisibility Rules For 12. To be divisible by 12 a number must be divisible by both 3 and 4. Example 48 is divisible by both 3 and 4 hence also divisibly by 12.
What is the easiest rule to use for numbers ending with 5?
The divisibility rule for 5 is the easiest as you only have to look for numbers ending with 5 or 0. If a number ends with 0 or 5 it is divisible by 5 else not. Example 55787625760 is divisible by 5 and 5551 is not.
What is the divisible by 10?
If a number has 0 in the ones place then it is divisible by 10. Example 100, 198970, 1080.
What are some examples of even numbers divisible by 2?
All even numbers, by definition, are divisible by 2. Some examples of numbers divisible by 2 are as follows. 24, 18, 68, 108, 184, 1020 . Divisibility Rule for 5. If a number ends in either a 0 or 5, it is divisible by 5. Some examples of numbers divisible by 5 are. 15, 35, 75, 125, 505, 1000.
What is the definition of divisibility?
Definition. Divisibility − A number m is said to be divisible by another number n. if n divides m completely without leaving a remainder. Divisibility Rule for 2. If a number ends in a 0, 2, 4, 6 or 8, it is divisible by 2. All even numbers, by definition, are divisible by 2.
