Divisibility Rules: Tests of Divisibility

Divisibility Rules: Here are various rules to check divisibility of numbers, which will allow you to quickly find out factors of large numbers.

A number is said to be divisible by another number if on dividing, the remainder is zero. There are ways to determine if a number is divisible by a certain number without carrying out the actual division.

Here are the various Divisibility Rules/Tests:

Divisibility by 2

A number is divisible by 2 if the last digit of the number (the one in the units place) is either 0 or 2, 4, 6, 8 (multiples of 2).

Examples: 10000,1252, 1994, 14626, 3818.

All of the above numbers are divisible by 2 because the digital in the units place is multiple of 2 or it is 0.

Divisibility by 3

A number is divisible by 3 if the sum of all the digits of the number is divisible by 3 (or is a multiple of 3).

Examples:

79851 is divisible by 3. The sum of all the digits comes to 30 which is divisible by 3. So, the number is divisible by 3.

Divisibility by 4

A number is divisible by 4 if the number formed by the last two-digits of the number (the digits in the tens and units place) is divisible by 4.

Example:

88312 is divisible by 4. The number formed by the last two digits (which happens to be 12) is divisible by 4. So, the entire number is also divisible by 4.

Divisibility by 5

A number is divisible by 5 if the last digit (the one in its units place) is 0 or 5.

Example:

75325 is divisible by 5 because the last digit is 5.

Divisibility by 6

A number is divisible by 6 if the number is divisible by both 2 as well as 3.

Example:

85806 is divisible by 6. The number is divisible by 2 as well as 3, so it is divisible by 6 also.

Divisibility by 8

A number is divisible by 8 if the number formed by its last three digits (the digits in the hundreds, tens and units place) is also divisible by 8.

Example:

54136 is divisible by 8. The number formed by its last three digits (which happens to be 136) is divisible by 8. So, the entire number is also divisible by 8.

Divisibility by 9

A number is divisible by 9 if the sum of all its digits of the number is divisible by 9.

Example:

3888 is divisible by 9. The sum of all the digits comes to 27 which is divisible by 9. So, the number is divisible by 9.

Divisibility by 10

A number is divisible by 10 if the last digit (the one in the units place) is 0.

Example:

50, 170, 700, 3000, 58970 are all divisible by 10 because the last digit of all these numbers is 0.

Divisibility by 11

A number is divisible by 11 if the difference between the sum of all the digits in the odd places and the sum of all the digits in the even places is a multiple of 11 or is zero.

Example:

2839155 is divisible by 11.

• Sum of all the digits in the even places = 5 + 9 + 8 = 22
• Sum of all the digits in the odd places = 5 + 1 + 3 + 2 =11
• Difference between the two sums = 22 – 11= 11, which is divisible by 11.

So, 2839155 is divisible by 11.