Divisibility rules, also known as divisibility criteria, are rules that let you know if a number can divide another in an exact manner. Thus, it's possible to know whether a number is a divisor of another, without having to actually do the calculations. In this blog you can learn the divisibility rules for 2, 3, 4, 5, 6, 7, 8, 9, 10, and other numbers.
- divisibility rules for 2
The number two divides all pair numbers, that is, all numbers that ends with the digits 0, 2, 4, 6 or 8.
example:
68 is pair, so, it's divisible by 2.
912 is pair, so it's also divisible by 2.
A number is divisible by 3, if the sum of its digits is a multiple of 3.
example:
- divisibility rules for 3
A number is divisible by 3, if the sum of its digits is a multiple of 3.
example:
The sum of the digits of 531 is 5 +3 +1 = 9.
9 is a multiple of 3, so 531 is divisible by 3
- divisibility rules for 4
A number is divisible by 4 if the sum of its units digit with the twice the tens digit, is a multiple of 4.
example:
In the number 7236, the sum of the units digit (6) with twice the number of tens (3) is 6+2x3 = 12
12 is multiple of 4, then 7236 is divisible by 4.
- divisibility rules for 5
A number is divisible by 5 if it ends in 0 or 5.
example:
345 ends in 5, so it is divisible by 5
- divisibility Rules for 6
A number is divisible by 6 if it is divisible by 2 and 3. So, just use the divisibility rules for 2 and 3 to verify.
example, consider the number 972 .
972 is a pair number, so it is divisible by 2 .
9 +7 +2 = 18, 18 is a multiple of 3, so 972 is divisible by 3.
Since 972 is divisible by 2 and 3, so it is also divisible by 6.
- divisibility rules for 8
A number is divisible by 8 if the number formed by its last three digits is divisible by 8 .
Example: In the number 4240, the number formed by the last three digits is 240. As 240:8 = 30, then 4240 is divisible by 8.
- divisibility rules for 9
A number is divisible by 9 if the sum of its digits is a multiple of 9 .
example : The sum of the digits of 693 is 6 +9 +3 = 18 .
18 is a multiple of 9, so 693 is divisible by 9
- divisibility by 10
A number is divisible by 10 if the last digit is a zero.
example: 83610
The number ends in zero, so it is divisible by 10 .
- divisibility Rules for 6
A number is divisible by 6 if it is divisible by 2 and 3. So, just use the divisibility rules for 2 and 3 to verify.
example, consider the number 972 .
972 is a pair number, so it is divisible by 2 .
9 +7 +2 = 18, 18 is a multiple of 3, so 972 is divisible by 3.
Since 972 is divisible by 2 and 3, so it is also divisible by 6.
- divisibility rules for 8
A number is divisible by 8 if the number formed by its last three digits is divisible by 8 .
Example: In the number 4240, the number formed by the last three digits is 240. As 240:8 = 30, then 4240 is divisible by 8.
- divisibility rules for 9
A number is divisible by 9 if the sum of its digits is a multiple of 9 .
example : The sum of the digits of 693 is 6 +9 +3 = 18 .
18 is a multiple of 9, so 693 is divisible by 9
- divisibility by 10
A number is divisible by 10 if the last digit is a zero.
example: 83610
The number ends in zero, so it is divisible by 10 .
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