math-and-code-tricks

Math and code tricks

Math Tricks

Divisibility Rules

Three

An integer is divisible by 3 if its digits sum to 3, 6 or 9. Continually sum the digits until there is only a single digit left, if this is a 3, 6, or 9, then the original number is divisible by 3.

E.g.:

16842
1 + 6 + 8 + 4 + 2 = 21
2 + 1 = 3
∴ 16842 is divisible by 3

9472
9 + 4 + 7 + 2 = 22
2 + 2 = 4
∴ 9472 is not divisible by 3

Nine

An integer is divisible by 9 if its digits sum to 9. Continually sum the digits until there is only a single digit left, if this is 9, then the original number is divisible by 9.

E.g.:

93874
9 + 7 + 8 + 7 + 5 = 36
3 + 6 = 9
∴ 93874 is divisible by 9

1565
1 + 5 + 6 + 5 = 17
1 + 7 = 8
∴ 1565 is not divisible by 9

Log Values

The following is how log values work.

• log_base(result) = power
• base^power = result

This can then be written as log_b(a) = c and rearranged to look like b^c = a, where

• a = argument
• b = base
• c = exponent

E.g:

10²=100
log₁₀(100) = 2