# Prime Factorization

Prime factorization is the multiplication of prime numbers to get the product.

Here are few examples to illustrate prime factorization

1. Find prime factorization of 48

Solution:

Using the factor tree the prime factors are:

The prime factorization of 48 = 2 × 2 × 2 × 2 × 3 = 2× 3 = 48

2. Find prime factorization of 56

Solution:

Using the factor tree the prime factors are:

The prime factorization of 56 = 2 × 2 × 2 × 7 =  2× 7 56

3. Find prime factorization of 96

Solution:

Factor tree the prime factors are:

The prime factorization of 96 = 2 × 2 × 2 × 2 × 2 × 3 = 2× 3 = 96

4. Find prime factorization of 64

Solution:

Factor tree the prime factors are:

The prime factorization of 64 = 2 × 2 × 2 × 2 × 2 ×2 = 2= 64

5. Find prime factorization of 78

Solution:

Using the factor tree the prime factors are:

The prime factorization of 78 = 2 × 2 × 13 = 2× 13 = 78

6. Find prime factorization of 120

Solution:

Using the factor tree the prime factors are:

The prime factorization of 96 = 2 × 2 × 2 × 3 × 5 = 23 × 3 × 5 = 120

7. Find prime factorization of 343

Solution:

Factor tree the prime factors are:

The prime factorization of 96 = 7 × 7 × 7 = 73 = 343

8. Find prime factorization of 360

Solution:

Factor tree the prime factors are:

The prime factorization of 360 = 2 × 2 × 2 × 3 × 3 × 5 = 23 × 32  × 5 = 360

9. Find prime factorization of 144

Solution:

The prime factorization of 360 = 2 × 2 × 2 × 2 × 3 × 3 = 2× 32 = 360

10. Find prime factorization of 150

Solution:

With the factor tree the prime factors are:

The prime factorization of 150 = 2 × 3 × 5 × 5 = 2 × 3 × 52 = 150

11. Find prime factorization of 125

Solution:

With the factor tree the prime factors are:

The prime factorization of 125 = 5 × 5 × 5 = 5= 125

12. Find prime factorization of 128

Solution:

With the factor tree the prime factors are:

The prime factorization of 64 = 2 × 2 × 2 × 2 × 2 ×2 × 2 = 2= 128

13. Find prime factorization of 243

Solution:

Using the factor tree the prime factors are:

The prime factorization of 243 = 3 × 3 × 3 × 3 × 3 = 35 = 243

14. Find prime factorization of 225

Solution:

With the factor tree the prime factors are:

The prime factorization of 225 = 5 × 5 × 3 × 3 = 5× 3= 225

15. Find prime factorization of 85

Solution:

With the factor tree the prime factors are:

The prime factorization of 85 = 5 × 17 = 85