Worked example 1
Find the prime factorization of 60.
Start by writing the calculation clearly: 60 = 2 × 30 = 2 × 2 × 15 = 2 × 2 × 3 × 5. So 60 = 2² × 3 × 5.
Answer: 2² × 3 × 5
Grade 6 Math · Topic 33
Prime Factorization
Every composite number can be written as a unique product of primes — its prime factorization. A factor tree is the easiest way to find it: keep breaking each composite into two smaller factors until every leaf is prime.
Lesson alignment: 6.NS.B.4 · Take your time. You can return to this lesson whenever you need it.
Explore visually
Build a prime factor tree
Split a composite number into factors until every branch ends in a prime number.
Think first: Which factor could you split first, and which numbers might end as prime leaves?
Ready? Reveal the model and try your prediction
Swipe horizontally to see the full diagram.
Turn on JavaScript to adjust this model. The examples and practice below work without it.
Follow the worked examples
Read each step, then cover the explanation and see if you can explain why it works.
Worked example 2
Find the prime factorization of 84.
Start by writing the calculation clearly: 84 = 2 × 42 = 2 × 2 × 21 = 2 × 2 × 3 × 7. So 84 = 2² × 3 × 7.
Answer: 2² × 3 × 7
Try a few on your own
Work these on paper first. Open “Check” when you are ready to compare your answer.
- 18 =
Check
2·3²
- 24 =
Check
2³·3
- 45 =
Check
3²·5
- 56 =
Check
2³·7
- 72 =
Check
2³·3²
- 100 =
Check
2²·5²
- 120 =
Check
2³·3·5
- 144 =
Check
2⁴·3²
Try this situation 1
Write 90 as a product of primes.
Show a worked solution
Answer: 2 × 3² × 5.
Start by writing the calculation clearly: 90 = 2 × 45 = 2 × 9 × 5 = 2 × 3 × 3 × 5 = 2 × 3² × 5.
Try this situation 2
Find the prime factorization of 150.
Show a worked solution
Answer: 2 × 3 × 5².
Start by writing the calculation clearly: 150 = 2 × 75 = 2 × 3 × 25 = 2 × 3 × 5 × 5.
Fresh questions · saved on this device
Practice this skill
Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.
Question 1 of 50 correct so far
Session complete
Check what you learned
Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.
Practice and finish
Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.
Your checkmark, skill-practice sessions, and best exit-check score are saved on this browser and device. The course page can download a progress report to share with a tutor or teacher.
More Grade 6 resources
Use these free materials if you want another explanation, extra paper practice, or a broader review.