Factors and prime numbers, explained
A factor of a number divides it exactly: 1, 2, 3, 4, 6 and 12 are the factors of 12. A prime has only two factors, 1 and itself, and every other whole number bigger than 1 can be made by multiplying primes. The pages below go in the order a class usually meets them.
Start with what a prime is. Then break a number into its primes with a factor tree or a factor ladder, whichever your school draws. Do it for two numbers and you get their highest common factor and their lowest common multiple.
- What is a prime number? Only 1 and the number itself divide it.
- How to tell if two numbers are coprime The only number that divides both is 1.
- How to find prime factors with a factor tree Split it, and split again, until every branch is prime.
- How to find prime factors with a factor ladder Divide by primes, down a column, until you reach 1.
- How to find the highest common factor (HCF) The biggest number that divides both.
- How to find the lowest common multiple (LCM) The smallest number both of them divide into.
Questions people ask
What is the difference between a factor and a multiple?
A factor goes into a number; a multiple is what you get by multiplying it. 3 is a factor of 12, and 12 is a multiple of 3. A number has only a few factors, but its multiples go on for ever: they are its times table.
Factor tree or factor ladder, which is right?
Both. They find the same primes, and only the drawing differs. Most English-speaking schools teach the tree first. The ladder keeps everything in one tidy column, and can take two numbers side by side.
What are prime factors used for?
Finding the highest common factor and the lowest common multiple, and through them simplifying fractions and adding fractions with different denominators.