--- title: "Factors, multiples, and primes" description: "Find all factor pairs for numbers to 100, list common factors and multiples, and tell whether a number is prime" canonical: https://lightmysky.com/learn/mathematics/factors-multiples-and-primes-mt_FHIAv6dfhU source: https://lightmysky.com/learn/mathematics/factors-multiples-and-primes-mt_FHIAv6dfhU.md retrieved: 2026-10-19 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Factors, multiples, and primes Find all factor pairs for numbers to 100, list common factors and multiples, and tell whether a number is prime Subject: Mathematics · Area: Multiplication & Division · Ages 9 to 11 Page: https://lightmysky.com/learn/mathematics/factors-multiples-and-primes-mt_FHIAv6dfhU ## Ready when they can - 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 ## Lesson: Factors, multiples, and primes 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. **Example.** 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). *(drawing: Skip count by 7: 7, 14, 21, 28, 35. Each landing spot is a multiple of 7.)* 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. **Recap.** 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. ## Practice 16 questions on this page, each with its working shown. ## Needs first - [Factor Pairs & Commutativity](https://lightmysky.com/learn/mathematics/factor-pairs-and-commutativity-mt_nZkL5-XjRX) ## Opens up - [Factors, multiples, squares and cubes (age 9+)](https://lightmysky.com/learn/mathematics/factors-multiples-squares-and-cubes-age-9-mt_0Wg5F97osg) - [Simplifying Fractions](https://lightmysky.com/learn/mathematics/simplifying-fractions-mt_b7T-CjOYUR) - [Fractions, Decimals & Percentages](https://lightmysky.com/learn/mathematics/fractions-decimals-and-percentages-mt_hlGKg5M7qJ) - [Factors, multiples, and primes (age 11+)](https://lightmysky.com/learn/mathematics/factors-multiples-and-primes-age-11-mt_xhoOWnhtHq) - [Ratio Notation](https://lightmysky.com/learn/mathematics/ratio-notation-mt_XWSGuFW7It) - [Prime numbers](https://lightmysky.com/learn/mathematics/prime-numbers-mt_y1XCVsIelg)