Math: Prime Factorization Trees
Breaking composite numbers into prime factors
Math: Prime Factorization Trees
Breaking composite numbers into prime factors
Math - Grade 4-5
- 1
Make a factor tree for 18. Write the prime factorization of 18.
Start by thinking of two numbers that multiply to make 18.
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. - 2
Make a factor tree for 24. Write the prime factorization of 24.
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. - 3
Complete this factor tree: 30 splits into 3 and 10. Then 10 splits into 2 and ___. Write the prime factorization of 30.
Find the number that multiplies by 2 to make 10.
The missing number is 5. The prime factorization of 30 is 2 × 3 × 5. - 4
Make a factor tree for 36. Write the prime factorization of 36.
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. - 5
Make a factor tree for 45. Write the prime factorization of 45.
Try starting with 9 × 5.
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. - 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.
The missing numbers are 2 and 2. The prime factorization of 56 is 2 × 2 × 2 × 7, or 2³ × 7. - 7
A student says the prime factorization of 20 is 4 × 5. Explain the mistake and write the correct prime factorization.
Prime factorization must use only prime numbers.
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. - 8
Make a factor tree for 50. Write the prime factorization of 50.
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. - 9
Which number has the prime factorization 2 × 3 × 7? Show how you know.
Multiply the prime factors together.
The number is 42 because 2 × 3 = 6, and 6 × 7 = 42. - 10
Make a factor tree for 64. Write the prime factorization of 64.
Keep dividing by 2 until every factor is prime.
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. - 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.
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. - 12
Make a factor tree for 75. Write the prime factorization of 75.
Try starting with 3 × 25.
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.