# Divisibility Tests

## Divide to Rule?

Division is fun

Numbers are like flowers. You should handle them carefully. Students start using the basic operations like addition and subtraction of numbers at tender age. They should learn division also. Most of them are afraid to divide numbers. We need to divide a number occasionally. You may be interested to learn new and short-cut methods. By learning simple tricks, you can easily succeed.

If a number a divides b exactly, we say a is a divisor of b, a is a factor of b or b is a multiple of a. But how do you know the given number is divisible by 17 or 19? Here you can learn these simple tests and teach your children to apply.

Mathematics is about pattern and structure. Division of numbers also has some interesting patterns. If you understand it, you will be a master in numerical manipulation.

## Test 1

If last digit of the number  is 0 or 5, then it is divisible by 5.

Eg. 410, 78345.

If last digit of the number  is 0, then it is divisible by 10.

Eg. 370, 567450.

If last two digits of the number  is 0, then it is divisible by 100.

Eg. 6400, 742300.

If last two digits of the number  is divisible by 25, then it is divisible by 25.

Eg. 3425, 739475.

If last three digits of the number  is divisible by 125, then it is divisible by 125.

Eg. 56125, 94375.

## Test 2

If last digit of the number is 0,2,4,6 or 8, then it is divisible by 2.

Eg. 356, 97358, 34560.

If last 2 digits of the number is divisible by 4, then it is divisible by 4.

Eg. 9524, 97308, 34560.

If last 3 digits of the number is divisible by 8, then it is divisible by 8.

Eg. 755240, 573008, 345808.

## Test 3

If sum of digits of the number is divisible by 3, then it is divisible by 3.

Eg. (i) 540, 5+4+0=9 and 9 is divisible by 3.

(ii) 673008, 6+7+3+0+0+8=24 and 24 is divisible by 3.

If sum of digits of the number is divisible by 9, then it is divisible by 9.

Eg. (i) 837, 8+3+7=18 and 18 is divisible by 9.

(ii) 673038, 6+7+3+0+3+8=27 and 27 is divisible by 9.

## Test 4

If the number is divisible by both 2 (refer test 2) and 3 (refer test 3), then it is divisible by 6.

Eg. (i) 378, Last digit is 8. So divisible by 2. 3+7+8=18 and 18 is divisible by 3.

(ii) 3690.

If the number is divisible by both 3 and 4, then it is divisible by 12.

Eg. (i) 4500  (ii) 6348.

If the number is divisible by both 3 and 5, then it is divisible by 15.

Eg. (i) 6510  (ii) 236205.

## Test 5

If sum of digits in odd places - sum of digits in even places is 0 or a multiple of 11, then the number is divisible by 11.

Eg. (i) 5610 since (5+1)-(6+0)=0 (ii) 22605 since (2+6+5)-(2+0)=11.

## Test 6

If number of tens added to TWO times number of units is divisible by 19, then the number is divisible by 19.

Eg. 342 since 34+2X2=38 is divisible by 19.

If number of tens added to THREE times number of units is divisible by 29, then the number is divisible by 29.

Eg. 377 since 37+3X7=58 is divisible by 29.

If number of tens added to FOUR times number of units is divisible by 13, then the number is divisible by 13.

Eg. 221 since 22+4X1=26 is divisible by 13.

If number of tens added to FIVE times number of units is divisible by 7, then the number is divisible by 7.

Eg. 259 since 25+5X9=70 is divisible by 7.

If number of tens added to TWELVE times number of units is divisible by 17, then the number is divisible by 17.

Eg. 442 since 44+12X2=68 is divisible by 17.