Lessons · Teaching · factors, multiples and primes
Factors, multiples and the numbers that have neither
A factor of a number divides it exactly; a multiple of a number is what you get by multiplying it. Factors are finite and sit at or below the number; multiples are infinite and sit at or above it. A prime has exactly two factors, itself and one, which is why one is not prime.
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In beta. This lesson was written for Hone and has not yet been checked by a state certification officer. Practice material, not professional advice. What that means.
What it is for
Every fraction question later is a factor question wearing different clothes. Simplifying needs a common factor, adding needs a common multiple, and a pupil who cannot list the factors of 24 will be stuck at both. This topic looks like trivia and is the foundation of the next stage.
How to think about it
Find factors in pairs, working up from one, and stop when the pair meets: 24 gives 1 and 24, 2 and 12, 3 and 8, 4 and 6, then 5 fails and 6 is already used, so you are done. Pairs stop you missing any and tell you exactly when to stop.
Worked example
Factors of 24 in pairs: 1x24, 2x12, 3x8, 4x6Eight factors, found in four pairs, with a clear stopping point.
Multiples of 6: 6, 12, 18, 24, 30, and on foreverMultiples do not stop. Factors do.
Primes to 20: 2, 3, 5, 7, 11, 13, 17, 192 is the only even prime, which surprises people every time.
1 has one factor, so it is not prime; 2 has exactly two, so it isPrime means exactly two factors, not 'only divisible by itself and one'.
Your turn
Name how many factors a prime number has.
A prime number has exactly factors
Solve one, graded on the server
The trap
Swapping the words. A pupil asked for factors of 8 who writes 8, 16, 24 has given multiples. The check is size: a factor is never bigger than its number, a multiple is never smaller.