Division

Mental Division Tricks

• divide by 5: multiply the number by 2 and remove a zero.

Mental trick: Divisibility

Divisible by 3 and 9

Sum up all the digits, and if that number is divisible by 3, then so is the original number

• ex. "is 231 divisible by 3?" can be restated as "is 6 (2+3+1) divisible by 3?"
• ex. "is 375 divisible by 9?" can be restataed as "is 15 divisible by 9?

Divisible by 6

Sum up all digits, and if that number is divisible by 3 AND is an even number, then the original number is divisible by 6

Divisible by 4

If the last 2 digits of a number are divisible by 4, then so is the whole number

• ex. "is 43,275 divisible by 4?" can be restated as "is 75 divisible by 4?"

A big 2-digit number

We can figure out if a big 2-digit number is divisible by 4 by taking the first digit, doubling it, then adding the second digit

• ex. "is 96 divisible by 4?" can be restated as "is 24 divisible by 4?
  • $(9*2) + 6 = 24$

Divisible by 8

Take the last 3 digits of the number and multiple the 100's column digit by $4$, the 10's column digit by $2$, and the 1's column digit by $1$, and sum the results.

• ex. 362,848:
  $$(4 x 8) + (2 x 4) + 8 = 48$$

48 is divisible by 8, therefore 362,848 is divisible by 8