Division

Number	Division Hint
2	All even numbers will divide exactly by two
3	Add up all the digits in any number. If the total will divide exactly by 3 then the original number will divide exactly by 3
4	If the last two digits of a number will divide exactly by 4 then the original number will divide exactly by 4.
5	If the last digit of a number is either 0 or 5 then the entire number will divide exactly by 5
6	If both of these are true - Add up all the digits in a number and the total will divide by 3 - The original number is an even number then the original number will divide exactly by 6
7	Double the last digit of original number and subtract this from the remainig digits. If your answer will divide exactly bt 7 then the original number will divide by 7. (You may have to repeat process to decide whenther answer will divide by 7)
8	If the last three digits of a number will divide exactly by 8 then the original number will divide exactly by 8.
9	Add up all the digits in any number. If the total will divide exactly by 9 then the original number will divide exactly by 9
10	If the last digit of a number is 0 then the number will divide exactly by 10
11	Add up "every other" digit in the number. Subtract the sum of the remaining digits. If the answer will divide exactly by 11 then the original number will divide exactly by 11
12	If both of these are true - Add up all the digits in your number. If the total will divide exactly by 3 - The last 2 digits of your number will divide exactly by 4 then your number will divide exactly by 12

Multiplication

Number	Multiplication Hint
2	Multiplying by two is identical to adding the number to itself.
4	Double the number and double your answer. (i.e. multiply by 2 and multiply by 2 again.)
5	Divide the number by 2 and then multiply by 10

Squaring Numbers

To square any number ending in ".5" --> Multiply (number - 0.5) by (number + 0.5) and add 0.25