Factors, Multiples & Primes

A factor of a number divides into it exactly, with no remainder. The factors of $12$ are $1, 2, 3, 4, 6, 12$.

A multiple is what you get by multiplying a number by $1, 2, 3, \dots$ The multiples of $4$ are $4, 8, 12, 16, 20, \dots$

A prime number has exactly two factors: $1$ and itself. So $7$ is prime; $12$ is not (it has six factors). Note that $1$ is not prime — it has only one factor.

Two useful pairings:

• The highest common factor (HCF) of $12$ and $18$ is the biggest number dividing both. Factors of $12$: $1,2,3,4,6,12$; of $18$: $1,2,3,6,9,18$; the largest shared one is $6$.
• The lowest common multiple (LCM) of $4$ and $6$ is the smallest number in both times-tables: $4,8,\mathbf{12}$ and $6,\mathbf{12}$, so the LCM is $12$.