Factor Pairs

Some numbers divide into another exactly, with nothing left over.

Factor is a number that divides into another number exactly.

Factors come in pairs

12 = 3 × 4, so 3 and 4 are a factor pair of 12.

Each pair is a rectangle

A factor pair of 12 is a rectangle with 12 squares: 1 × 12, 2 × 6, or 3 × 4.

Search in order

Try 1, then 2, then 3, and so on. Working in order means none get missed.

Factors are rectangle sides

The factor pairs of 24 are 1×24, 2×12, 3×8 and 4×6. Each pair is a rectangle you could build from 24 squares. Numbers with many factor pairs make many rectangle shapes; numbers with few make few.

Find them systematically

Start at 1 and test each number in turn: does 1 divide 24? Yes, partner 24. Does 2? Yes, partner 12. Does 3? Yes, partner 8. Does 4? Yes, partner 6. Does 5? No. Then 6, whose partner 4 you already have — so you can stop. Working upwards means you never miss one.

Knowing when to stop

Once the two numbers in a pair meet or cross, every remaining pair is a repeat of one you have found. For 24 that happens between 4×6 and 6×4. This is why the search is short even for fairly large numbers.

What factors are for

Factors are how you simplify a fraction, find a common denominator, and split a number for easier multiplication. They look like a curiosity in this lesson and turn out to be the machinery behind most of the fraction work in Grades 4 and 5.