Factors and multiples
Factors divide a number exactly; multiples are what you reach by counting in a number.
Two words sit at the heart of this topic, and they pull in opposite directions.
A factor of a number divides into it exactly, with nothing left over. The factors of 12 are — each one divides 12 with no remainder.
A multiple of a number is what you get by multiplying it by a whole number. The multiples of 12 are — the answers in its times table.
A neat way to keep them apart: factors are smaller than or equal to the number and there are only a few of them, while multiples are equal to or bigger than the number and the list goes on forever.
To list factors without missing any, search in pairs. For 12: , , — work upwards until the pair meets in the middle.
- A factor divides a number exactly, with no remainder.
- A multiple is a number multiplied by a whole number.
- Find factors in pairs so none are missed.
- There are finitely many factors but infinitely many multiples.