Math: Prime Factorization Trees Worksheet

Question 1

Make a factor tree for 18. Write the prime factorization of 18.

Accepted Answer

The prime factorization of 18 is 2 × 3 × 3, or 2 × 3². One factor tree is 18 split into 2 and 9, then 9 split into 3 and 3.

Question 2

Make a factor tree for 24. Write the prime factorization of 24.

Accepted Answer

The prime factorization of 24 is 2 × 2 × 2 × 3, or 2³ × 3. One factor tree is 24 split into 6 and 4, then 6 split into 2 and 3, and 4 split into 2 and 2.

Question 3

Complete this factor tree: 30 splits into 3 and 10. Then 10 splits into 2 and ___. Write the prime factorization of 30.

Accepted Answer

The missing number is 5. The prime factorization of 30 is 2 × 3 × 5.

Question 4

Make a factor tree for 36. Write the prime factorization of 36.

Accepted Answer

The prime factorization of 36 is 2 × 2 × 3 × 3, or 2² × 3². One factor tree is 36 split into 6 and 6, then each 6 split into 2 and 3.

Question 5

Make a factor tree for 45. Write the prime factorization of 45.

Accepted Answer

The prime factorization of 45 is 3 × 3 × 5, or 3² × 5. One factor tree is 45 split into 9 and 5, then 9 split into 3 and 3.

Question 6

Complete this factor tree: 56 splits into 7 and 8. Then 8 splits into 2 and 4. Then 4 splits into ___ and ___. Write the prime factorization of 56.

Accepted Answer

The missing numbers are 2 and 2. The prime factorization of 56 is 2 × 2 × 2 × 7, or 2³ × 7.

Question 7

A student says the prime factorization of 20 is 4 × 5. Explain the mistake and write the correct prime factorization.

Accepted Answer

The mistake is that 4 is not a prime number. Since 4 = 2 × 2, the correct prime factorization of 20 is 2 × 2 × 5, or 2² × 5.

Question 8

Make a factor tree for 50. Write the prime factorization of 50.

Accepted Answer

The prime factorization of 50 is 2 × 5 × 5, or 2 × 5². One factor tree is 50 split into 2 and 25, then 25 split into 5 and 5.

Question 9

Which number has the prime factorization 2 × 3 × 7? Show how you know.

Accepted Answer

The number is 42 because 2 × 3 = 6, and 6 × 7 = 42.

Question 10

Make a factor tree for 64. Write the prime factorization of 64.

Accepted Answer

The prime factorization of 64 is 2 × 2 × 2 × 2 × 2 × 2, or 2⁶. Since 64 is a power of 2, all of its prime factors are 2.

Question 11

Two students made factor trees for 48. One started with 6 × 8. The other started with 4 × 12. Will they get the same prime factorization? Explain.

Accepted Answer

Yes, they will get the same prime factorization. No matter which factor pair they start with, the prime factorization of 48 is 2 × 2 × 2 × 2 × 3, or 2⁴ × 3.

Question 12

Make a factor tree for 75. Write the prime factorization of 75.

Accepted Answer

The prime factorization of 75 is 3 × 5 × 5, or 3 × 5². One factor tree is 75 split into 3 and 25, then 25 split into 5 and 5.

Math: Prime Factorization Trees

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