Prime Factorization — Worksheet

Prime Factorization

Worksheet

Open the Prime Factorization module. In Factor tree, set the number and split the branches until every leaf is prime. Switch to GCF & LCM when a question says so.

Name: Date:

Part A: Build a tree

1. In Factor tree, set the number to 60 and split until every leaf is prime. Which is the prime factorization? 1 pt
  • 2 × 2 × 3 × 5
  • 2 × 3 × 5
  • 4 × 3 × 5
  • 2 × 2 × 15
2. Set the number to 36 and finish the tree. How many prime factors does 36 have in total, counting repeats? 1 pt
Answer:
3. Set the number to 48 and finish the tree. 48 = 2^? × 3. What is the exponent of 2? 1 pt
Answer:
4. Set the number to 30 and finish the tree. Which is its prime factorization? 1 pt
  • 2 × 3 × 5
  • 3 × 10
  • 2 × 15
  • 5 × 6
5. Set the number to 97. What is its prime factorization? (Build the tree and see.) 1 pt

Part B: GCF and LCM from primes

6. Switch to GCF & LCM and set the numbers to 12 and 18. What is the greatest common factor? 1 pt
  • 2
  • 3
  • 6
  • 36
7. Still with 12 and 18, what is the least common multiple? 1 pt
  • 6
  • 36
  • 54
  • 216
8. Set the numbers to 20 and 30. What is the greatest common factor? 1 pt
Answer:
9. Still with 20 and 30, what is the least common multiple? 1 pt
Answer:
10. Set the numbers to 8 and 9. What is the greatest common factor? 1 pt
Answer:

Part C: Reasoning

11. Explain how the prime factorizations of two numbers give their greatest common factor and their least common multiple. 2 pts