Division Shortcuts

1
Cheat codes for solving division problems without
the use of a calculator

• Division Shortcuts

2
If the last digit is even, the number is
divisible by 2.
3
2,245,432 is even therefore is divisible by 2
4
If the sum of the digits is divisible by 3, the
number is also.
5
For example 12,123 (121239) 9 is divisible
by 3, therefore 12,123 is too!
6
If the last two digits form a number divisible by
4, the number is also.
7
For example 358,912 ends in 12 which is
divisible by 4, thus so is 358,912
8
If the last digit is a 5 or a 0, the number is
divisible by 5.
9
If the number is divisible by both 3 and 2, it
is also divisible by 6.
10
Take the last digit, double it, and subtract it
from the rest of the number if the answer is
divisible by 7 (including 0), then the number
is also.
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Is 854 divisible by 7?Number A 85Number B
4Number A (2 Number B) 85 - 2 4 7777
is most certainly divisible by 7, therefore 854
is also divisible by 7
12
If the last three digits form a number
divisible by 8, then so is the whole number.
13
Example 6,008 - The last 3 digits are divisible
by one, therefore, so is 6,008.
14
If the sum of the digits is divisible by 9, the
number is also.
15

• Example 357 (Double the 7 to get 14. Subtract 14
  from 35 to get 21 which is divisible by 7 and we
  can now say that 357 is divisible by 7.

16
For example 43,785 (4378527) 27 is
divisible by 9, therefore 43,785 is too!
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If the number ends in 0, it is divisible by 10.
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Alternately add and subtract the digits from left
to right. If the result (including 0) is
divisible by 11, the number is also.
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Example to see whether 365,167,484 is divisible
by 11, start by subtracting 3-65-16-74-84
0 therefore 365,167,484 is divisible by 11.
20
If the number is divisible by both 3 and 4, it
is also divisible by 12.
21
If the sum of the digits in the odd places
subtracted by the sum of the digits in the even
places is divisible by 13
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13- Delete the last digit from the number, then
subtract 9 times the deleted digit from the
remaining number. If what is left is divisible by
13, then so is the original number.
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For example 16,313,349 1631334 -81
1631253 163125 27 163098 16309 72
16237 1623 63 1560 156 0 156 13 12
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25 - if the number formed by the last 2 digits
is divisible by 25 or both are zeros 25, 50, 75,
00
25
125- if the last three digits are divisible by
125 or all are zeros example 125, 250, 375,
500, 625, 750, 875, 1,000
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To divide by 10 or a power of 10, move the
decimal to the left or right Example 2,340 10
234 ( 1 place left) 234 100 2.34
234 0.01 23,400 2.34
0.1 23.4
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To divide by 5- multiply by 2 and divide by 10.
If a zero can be removed, divide first. Example
240 5 24 x 2 48 1,200 5 120 x 2 240
28

• If the last digit is not a zero, multiply first,
  then move the decimal one place to the left.
• Example 23 5
• 23 x 2 10 4.6
• 124 5 124 x 2 10 24.8

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• To divide by 25- multiply by 4 and divided by
  100. Use the same procedure as before for removal
  of zeros or placement of the decimal.

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• 600 25 6 x 4 24
• 2,300 25 23 x 4 92
• 212 25 212 x 4 100 8.48

31

• To divide by 125 multiply by 8 and divide by
  1,000.
• Example
• 7,000 125 7 x 8 56
• 12,000 125 12 x 8 96
• 2,011 125 2,011 x 8 1,000 16. 088

32

• List the numbers by which each of the following
  is divisible. Test for 2, 3, 4, 5, 6, 7, 8, 9,
  10, 11, 12, 13, 25, and 125.

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• 576
• 2,3,4,6,8,9,
• 435
• 3, 5
• 132,132
• 2,3,4,6,7,11,12,13
• 225
• 3,5,9,25