Division Rules

Question 1

How do you know whether something is divisible by 3?

Answer 1

Add up all the digits together. If the sum of the digits is divisible by three, than the number is too.

If the result of the adding up of the digits has two or more digits, add those digits together and take it from there.

Question 2

How do you know whether something is divisible by 4?

Answer 2

Look at the last two digits of the number. If they are divisible by 4, then the number is too.

Question 3

How do you know whether a number is divisible by 5?

Answer 3

If the number ends in a 5 or 0 it is divisible by 7

Question 4

How do you know whether something is divisible by 6 or not?

Answer 4

Check if the number is divisible by 2 AND 3. If it is, than the number can be divided.

Question 5

How do you tell if a number can be divided by 7?

Answer 5

Take the last digit, double it and subtract it from the rest of the number. If you get a number that is divisible by 7 (including 0), then the original number is divisible by 7. If you are still unsure about the new number, apply the rule again.

Or just use the old division method.

Question 6

How do you tell if a number is divisible by 8?

Answer 6

Check the last three digits. Since 1000 is divisible by 8, if the last three digits of a number are divisible by 8, then so is the whole number.

How can you tell whether the last three digits are divisible by 8? Phillip McReynolds answers:

If the first digit is even, the number is divisible by 8 if the last two digits are. If the first digit is odd, subtract 4 from the last two digits; the number will be divisible by 8 if the resulting last two digits are. So, to continue the last example, 33333888 is divisible by 8 because the digit in the hundreds place is an even number, and the last two digits are 88, which is divisible by 8. 33333886 is not divisible by 8 because the digit in the hundreds place is an even number, but the last two digits are 86, which is not divisible by 8.

All this is cited from http://mathforum.org/k12/mathtips/division.tips.html

Question 7

How can you tell if a number is divisible by 9?

Answer 7

Add the digits. If the sum of the digits is divisible by 9, then the original number is too.

Question 8

How can you tell whether a number is divisible by 10?

Answer 8

If the number ends in 0, it is divisible by 10.

Question 9

How do you tell whether a number is divisible by 11?

Answer 9

Take any number, such as 365167484.

Add the first, third, fifth, seventh,.., digits…..3 + 5 + 6 + 4 + 4 = 22

Add the second, fourth, sixth, eighth,.., digits…..6 + 1 + 7 + 8 = 22

If the difference, including 0, is divisible by 11, then so is the number.

22 - 22 = 0 so 365167484 is evenly divisible by 11.

Cited from http://mathforum.org/k12/mathtips/division.tips.html