Mathematics Tips & Tricks: Division

How you know when a number can be evenly divided by the certain numbers? By evenly means that the quotient has no remainder or you get an exact whole number.

Here’s a quick way to know when a number can be evenly divided by these certain numbers:

A number can be evenly divided by:

• 10 if the number ends in 0

Examples:

1) 500 / 10 = 50

2) 2750 / 10 = 275

3) 5240 / 10 = 520

• 9 when the digits are added together and the total is evenly divisible by 9

Examples:

1) 522 ==> 5+2+2 = 9 ; Since 9 is divisible by 9  (or a multiple of 9), then 522 can be evenly divided by 9.

522 / 9  = 58

2) 84213 ==> 8+4+2+1+3 = 18: Since 18 is divisible by 9 ( or a multiple of 9), then 84213 can be evenly divided by 9.

84213 / 9 = 9357

3) 50045 ==> 5+0+0+4+5 =  14: Since 14 is not divisible by 9, then 50045 cannot be evenly divided by 9.

• 8 if the last three digits are evenly divisible by 8 or are 000

Examples:

1) 71024 ==> the last 3 digits 024 are evenly divisible by 8 so 71024 can be evenly divided by 8.

71024 / 8 = 8878

2) 5027000 ==> the last 3 digits are 000, then 5027000 can be evenly divided by 8.

5027000 / 8 = 628375

3) 2000 ==> the last digits are 000, the 2000 can be evenly divided by 8.

2000 / 8 = 250

• 6 if it is an even number and when the digits are added together the answer is evenly divisible by 3

Examples:

1)  2532 ==> Is it even number? Yes! ; 2+5+3+2 = 12 : Since 12 is a multiple of 3, then 2532 can be evenly divided by 6.

2532 / 6 = 422

2)  984 ==> Is it even number? Yes! : Is 9+8+4 = 21 a multiple of 3? Yes!  (3x7 = 21)

984 / 6 = 164

• 5 if it ends in a 0 or 5

This is easy. Any number with 0 or 5 at the end can be evenly divided by 5.

Examples:

1) 510 ==> 510 / 5 = 102

2) 5355 ==> 5355 / 5 = 1071

3) 20035 ==> 20035 / 5 = 4007

• 4 if it ends in 00 or a two digit number that is evenly divisible by 4

Examples:

1)  4800 ==> 4800 / 4 = 1200

2) 724 ==> the last digits 24 is a multiple (4x6=24) of 4 so 724 can be evenly divided by 4.

724 / 4 = 181

3) 6816 ==> 16 is a multiple of 4 (4x4=16) then 6816 can be evenly divided by 4.

6816 / 4 = 1704

• 3 when the digits are added together and the result is evenly divisible by the number 3

Examples:

1) 56451 ==> 5+6+4+5+1 = 21: Is 21 divisible by 3? Yes! Then 56451 can be evenly divided by 3.

56451 / 3 = 18817

2) 300342 ==> 3+0+0+3+4+2 = 12: Is 12 divisible by 3? Yes! Then 300342 can be evenly divisible by 3.

300342 / 3  = 100114

3) 522 ==> 5+2+2 = 9; Since 9 is divisible by 3, then 522 can be evenly divided by 3.

522 / 3 = 174

• 2 if it ends in 0, 2, 4, 6, or 8

Like 5, this is very easy to understand. Any number with 0, 2, 4, 6 & 8 at the end, can be evenly divided by 2.

Examples:

1) 2010 ==>  2010 / 2 = 1005

2) 278 ==> 278 / 2 = 139

3) 62456 ==> 62456 / 2 = 31228