Factors, multiples, and primes
Find all factor pairs for numbers to 100, list common factors and multiples, and tell whether a number is prime
What a learner can do afterwards
- List all factor pairs of 36: (1,36), (2,18), (3,12), (4,9), (6,6)
- State the first five multiples of 7
- Find the common factors of 24 and 36
- Find all common factors of 36 and 48
- Identify the first three common multiples of 6 and 8
- Determine whether a given number (e.g. 97) is prime and justify the reasoning
1 · Read
You already know a factor pair multiplies to make a number. To find every factor pair, start at 1 and count up one number at a time. Check if each number divides evenly, and write down its partner. Once the two numbers in a pair meet or swap places, you have found them all.
Find every factor pair of 36. Start at 1: 1 x 36. Then 2: 2 x 18. Then 3: 3 x 12. Then 4: 4 x 9. Try 5: 36 does not divide evenly by 5, so skip it. Then 6: 6 x 6. The numbers have met at 6, so the search is done: (1,36), (2,18), (3,12), (4,9), (6,6).
Two numbers can share factors and share multiples. To find common factors, list the factors of each number, then pick out the ones that appear on both lists. To find common multiples, list the multiples of each number and pick out the ones that appear on both lists.
A prime number is greater than 1 and has only one factor pair: 1 and itself. So run the same factor-pair search, and if the only pair you find is 1 times the number, the number is prime. The number 1 is not prime: its only pair is 1 times 1, and a prime needs a pair with a number bigger than 1. Numbers like 4, 6, and 9 are not prime, because the search turns up a second pair before the numbers meet.
Find factor pairs by counting up until the pairs meet, compare lists to spot common factors and multiples, and a number greater than 1 is prime only when its one factor pair is 1 and itself.
Two readings and eight practice questions were written for this topic. The videos are linked from their original sources.
2 · Watch
Take it off screen
Where it sits
16 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.