Test of Divisibility For One and Two Digits

Test of Divisibility By Two

A number is divisible by 2, if its last digit is even number or Zero

Example1

Is 350 divisible by 2 ?

Last digit of 350 is Zero. So this number is divisible by 2

Example2

Is 2562 divisible by 2 ?

Last digit of 2562 is even number. So this number is divisible by 2

Test of Divisibility By Three

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

Example1

Is 642 divisible by 3 ?

Sum of the digits of 642 is 6 + 4 + 2 = 12. Again 12 is divisible by 3.Hence this number is divisible by 3.

Example2

Is 8931 divisible by 3 ?

Sum of the digits of 8931 is 8 + 9 + 3 + 1 = 21. Again 21 is divisible by 3.Hence this number is divisible by 3.

Test of Divisibility By Four

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

Example1

Is 872 divisible by 4 ?

Last 2 digits of 872 is 72, is 72 is divisible by 4. Hence 872 is divisible by 4.

Example2

Is 5348 divisible by 4 ?

Last 2 digits of 5348 is 48, is 48 is divisible by 4. Hence 5348 is divisible by 4.

Test of Divisibility By Five

A number is divisible by 5,if the last digit is either 5 or 0.

Example1

Is 985 divisible by 5 ?

Last digit of 985 is 5. Hence 985 is divisible by 5.

Example1

Is 1690 divisible by 5 ?

Last digit of 1690 is zero. Hence 1690 is divisible by 5.

Test of Divisibility By Six

A number is divisible by 6, if the number is divisible by 2 and 3.

Example1

Is 636 divisible by 6 ?

636 is divisible by 2 and also 636 is divisible by 3.Hence 636 is divisible by 6.

Example2

Is 2268 divisible by 6 ?

2268 is divisible by 2 and also 2268 is divisible by 3.Hence 2268 is divisible by 6.

Test of Divisibility By Seven

Pohlman-mass method

Example1

Number 234 divisible by 7 ?

Split the number as 23|4

Subtract twice unit digit from rest.

23 - 8 = 15

Repeat the process.

1|5

1 - 10 = -9.

This is not divisible by 7.

Hence 234 is not divisible by 7.

Example2

Number 4823 divisible by 7 ?

482|3

482 - 6 = 476

47|6

47 - 12 = 35

3|5

3 - 10 = -7

This is divisible by 7.

The number 4823 is divisible by 7.

Test of Divisibility By Eight

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

Example1

Is 2192 divisible by 8 ?

Last three digits of 2192 is 192. Since 192 is divisible by 8. Hence 2192 is divisble by 8.

Example2

Is 9128 divisible by 8 ?

Last three digits of 9128 is 128. Since 128 is divisible by 8. Hence 9128 is divisble by 8.

Test of Divisibility By Nine

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

Example1

Is 6453 divisible by 9 ?

Sum of 6453 is 6 + 4 + 5 + 3 = 18. Since 18 is divisible by 9. Hence 6453 is divisible by 9.

Example2

Is 8640 divisible by 9 ?

Sum of 8640 is 8 + 6 + 4 + 0 = 18. Since 18 is divisible by 9. Hence 8640 is divisible by 9.

Test of Divisibility By Ten

A number is divisible by 10, if the last digit is zero.

Example1

Is 3960 divisible by 10 ?

Last digit of 3960 is zero.Hence 3960 is divisble by 10.

Example2

Is 6770 divisible by 10 ?

Last digit of 6770 is zero.Hence 6770 is divisble by 10.

Test of Divisibility By Eleven

A number is divisible by 11,

if the sum of digits in the odd places and sum of digits in even places are equal or differ by a multiple of 11.

Example1

Is 209 divisible by 11 ?

Sum the values that present in the odd places. 2 + 9 = 11. so 11 is divisible by 11.Hence 209 is divisible by 11.

Example2

Is 3564 divisible by 11 ?

Find sum of digits in even places are equal.

Odd place value: 3564 = 3 + 6 = 9 and Even place value: 5 + 4 = 9 .

Here sum of digits in odd and even places are equal.Hence 3564 is divisible by 11.

Test of Divisibility By Twelve

A number is divisible by 3 and by 4.

Example1

Is 324 divisible by 12 ?

324 is divisible by 3 and 4.Hence 324 is divisible by 12.

Test of Divisibility By Thirteen

Add 4 times the last digit to the rest.

Example1

Is 637 divisible by 13 ?

637: 63 + 7 x 4 = 91, 9 + 1 x 4 = 13.Hence 637 is divisible by 13.

Test of Divisibility By Fourteen

A number is divisible by 2 and by 7.

Example1

Is 224 divisible by 14 ?

224: it is divisible by 2 and by 7.Hence 224 is divisible by 14.

Test of Divisibility By Fifteen

A number is divisible by 3 and by 5.

Example1

Is 390 divisible by 15 ?

390: it is divisible by 3 and by 5.Hence 390 is divisible by 15.

Test of Divisibility By Sixteen

Add the last two digits to four times the rest.

Example1

Is 176 divisible by 16 ?

176: 1 x 4 + 76 = 80. Hence 176 is divisible by 16.

Test of Divisibility By Seventeen

Subtract 5 times the last digit from the rest.

Example1

Is 221 divisible by 17 ?

221: 22 - 1 x 5 = 17. Hence 221 is divisible by 17.

Test of Divisibility By Eighteen

A number is divisible by 2 and by 9.

Example1

Is 342 divisible by 18 ?

342: it is divisible by 2 and by 9. Hence 342 is divisible by 18.

Test of Divisibility By Nineteen

Add twice the last digit to the rest.

Example1

Is 437 divisible by 19 ?

437: 43 + 7 x 2 = 57. Hence 437 is divisible by 19.

Test of Divisibility By Twenty

If the number formed by the last two digits is divisible by 20..

Example1

Is 480 divisible by 20 ?

480: 80 is divisible by 20. Hence 480 is divisible by 20.

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