Divisibility Rules, Factors and Multiples

Divisibility rules

By 2

last digit is 0, 2, 4, 6, or 8

By 3

sum of digits is divisible by 3

By 4

last two digits form a multiple of 4

By 5

last digit is 0 or 5

By 6

divisible by 2 and by 3

By 7

rest of number - 2 \times last digit is divisible by 7

By 8

last three digits form a multiple of 8

By 9

sum of digits is divisible by 9

By 10

last digit is 0

By 11

d_{1} - d_{2} + d_{3} - d_{4} + \dots is divisible by 11

By 12

divisible by 3 and by 4

GCF times LCM

GCF (a, b) \times LCM (a, b) = a \times b

a, b whole numbers

Number of factors

N = p_{1}^{a} p_{2}^{b} p_{3}^{c} \Rightarrow (a + 1) (b + 1) (c + 1) factors

p₁, p₂, p₃ different primes

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