Unit 5: Factors, Multiples, and Primes
The building blocks of whole numbers: factors, multiples, primes, and the two tools — GCF and LCM — built from them.
6 topics · 24 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
What a Factor Is
- How it worksHow do you find every factor of 24 by testing which numbers divide it evenly?
- Worked exampleFind all the factors of 36 by checking which numbers divide it with no remainder.
- Common mistakeWhy doesn't a bigger number like 17 always have more factors than a smaller number like 12?
- Ties togetherHow does finding the factors of a number connect to dividing it with no remainder?
Your turn1 of 2
Ravi arranges 7 times 7 stickers into 7 equal rows to check that 7 divides evenly into the total. How many stickers end up in each row?What a Multiple Is
- Worked exampleFind the first six multiples of 7.
- Common mistakeWhy doesn't a multiple of 4 have to be bigger than every multiple of 3?
- Going furtherWhat happens to the list of multiples of 6 if you start counting from 60 instead of 0?
Your turn1 of 2
Tom is skip-counting by 9s. What is the 7th multiple of 9 he says?Prime and Composite Numbers
- How it worksHow do you decide if 29 is prime by checking whether any smaller number divides it evenly?
- Common mistakeWhy isn't every odd number automatically prime?
- Worked exampleFind whether 51 is prime or composite by testing its possible factors.
- Going furtherWhat happens to your test for primeness if the number you're checking is 97 instead of 29?
- Ties togetherHow does knowing a number is composite connect to being able to list its factors?
Your turn1 of 2
Is 51 prime or composite?Finding Primes with the Sieve of Eratosthenes
- How it worksHow does crossing out every multiple of 2 on a number grid clear out half the numbers at once?
- How it worksHow do you keep crossing out multiples of 3, 5, and 7 on a hundred grid to leave only primes?
- Worked exampleFind every prime number between 1 and 50 using the sieve of Eratosthenes.
- Common mistakeWhy doesn't crossing out a number's multiples mean you also cross out the number itself?
Your turn1 of 2
Using the sieve of Eratosthenes, you cross out every multiple of 2, then every multiple of 3, on a number grid. Does this cross out the number 2 itself?Greatest Common Factor
- How it worksHow do you list the factors of 20 and 30 side by side to spot their greatest common factor?
- Worked exampleFind the greatest common factor of 24 and 36.
- Ties togetherHow does the greatest common factor connect to simplifying a fraction like 8 over 12?
Your turn1 of 2
Amara is grouping 15 times 2 red beads and 15 times 3 blue beads into equal-sized bags, with none left over. What is the biggest bag size she can use?Least Common Multiple
- How it worksHow do you list multiples of 6 and 8 side by side to find their least common multiple?
- Common mistakeWhy doesn't multiplying two numbers together always give you their least common multiple?
- Common mistakeWhy isn't the least common multiple of 4 and 6 the same as their greatest common factor?
- Worked exampleFind the least common multiple of 5 and 8.
- Going furtherWhat happens to the least common multiple of 6 and 9 if you replace 9 with 12?
Your turn1 of 2
A bus on one route leaves every 11 times 2 minutes, and a bus on another route leaves every 11 times 3 minutes. If they just left together, how many minutes until they leave together again?