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# Divisibility Test For Numbers From 2 To 15

October 5, 2020

Divisibility Test for 2

A number is divisible by 2, if it is an even number, i.e., the number ends in 0, 2, 4, 6 or 8.

e.g., 562, 7864, 56436 are all divisible by 2

Divisibility Test for 3

A number is divisible by 3, if the sum of its digits is divisible by 3.

e.g., 492318 is divisible by 3, since 4 + 9 + 2 + 3 + 1 + 8 = 27 is divisible by 3.

In fact 27 also, you can check by adding the digits: 2 + 7 = 9 is divisible by 3.

Divisibility Test for 4

A number is divisible by 4, if a number formed by the last two digits is divisible by 4.

e.g., 2536 is divisible by 4, since 36 is divisible by 4.

It is because 100 and multiples of 100 are divisible by 4.

2536 = 2500 + 36 = 25 ✖ 100 + 36

25 ✖ 100 is a multiple of 100, hence 2500 is divisible by 4 and 36 (number formed by last two digits) is divisible by 4, therefore, 2500 + 36 = 2536 is divisible by 4.

Divisibility Test for 5

A number is divisible by 5, if it ends in 0 or 5.

e.g., 430, 675, 67320 are all divisible by 5.

Divisibility Test for 6

A number is divisible by 6, if it is an even number (ends in 0, 2, 4, 6 or 8) and the sum of digits is divisible by 3.

e.g., 4896 is divisible by 6, since it is an even number (ending in 6) and 4 + 8 + 9 + 6 = 27 is divisible by 3.

Divisibility Test for 7

Steps to check divisibility by 7

• Multiply last digit by 2
• Subtract the result from the remaining digits (leaving the last digit)
• Repeat the process

In 5887,

The last digit is 7. 7 ✖ 2 = 14

Remaining digits are 588: 588 – 14 = 574

The last digit is 4: 4 ✖ 2 = 8

Remaining digits are 57: 57 – 8 = 49

Since, 49 is divisible by 7, therefore, 5887 is divisible by 7

Divisibility Test for 8

A number is divisible by 8, if a number formed by the last three digits is divisible by 8.

e.g., 2536 is divisible by 8, since 536 is divisible by 8.

It is because 1000 and multiples of 1000 are divisible by 8.

2536 = 2000 + 536 = 2 ✖ 1000 + 536

2 ✖ 1000 is a multiple of 1000, hence 2000 is divisible by 8 and 536 (number formed by last three digits) is divisible by 8, therefore, 2000 + 536 = 2536 is divisible by 8.

Divisibility Test for 9

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

e.g., 492318 is divisible by 9, since 4 + 9 + 2 + 3 + 1 + 8 = 27 is divisible by 9.

In fact 27 also, you can check by adding the digits: 2 + 7 = 9 is divisible by 9.

Divisibility Test for 10

A number is divisible by 10, if it ends in 0.

e.g., 560, 784320, 34800 are all divisible by 10.

Divisibility Test for 11

To check whether a number is divisible by 11, add and subtract digits in an alternating pattern (add digit, subtract next digit, add next digit, …). If the answer is 0 or divisible by 11, then the original number is divisible by 11.

e.g., 463254 is divisible by 11, since + 4 – 6 + 3 – 2 + 5 – 4 = 0.

You can also check by reversing the pattern: – 4 + 6 – 3 + 2 – 5 + 4 = 0.

Divisibility Test for 12

A number is divisible by 12, if it is divisible by 3 and 4 both, i.e., if the sum of its digits is divisible by 3 and the number formed by the last two digits is divisible by 4.

e.g., 463248 is divisible by 12, as sum of its digits 4 + 6 + 3 + 2 + 4 + 8 = 27 is divisible by 3 and the number formed by last two digits i.e., 48 is divisible by 4.

Divisibility Test for 13

Steps to check divisibility by 13

• Multiply last digit by 4
• Add the result with the remaining digits (leaving the last digit)
• Repeat the process

In 7501,

The last digit is 1. 1 ✖ 4 = 4

Remaining digits are 750: 750 + 4 = 754

The last digit is 4. 4 ✖ 4 = 16

Remaining digits are 75: 75 + 16 = 91

Since, 91 is divisible by 13, therefore, 7501 is divisible by 13

Divisibility Test for 14

A number is divisible by 14, if it is divisible by 2 and 7 both.

e.g., 38766 is divisible by 2 and 7 both, hence it is divisible by 14.

Divisibility Test for 15

A number is divisible by 15, if it is divisible by 3 and 5 both.

e.g., 38775 is divisible by 3 and 5 both, hence it is divisible by 15.

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