# 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^{4 }× 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^{3 }× 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^{5 }× 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^{6 }= 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^{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 = 2^{3} × 3 × 5 = 120

**7. Find prime factorization of 343**

**Solution:**

Factor tree the prime factors are:

The prime factorization of 96 = 7 × 7 × 7 = 7^{3} = 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 = 2^{3} × 3^{2} × 5 = 360

**9. Find prime factorization of 144**

**Solution:**

The prime factorization of 360 = 2 × 2 × 2 × 2 × 3 × 3 = 2^{4 }× 3^{2} = 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 × 5^{2} = 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^{3 }= 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^{7 }= 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 = 3^{5} = 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^{2 }× 3^{2 }= 225

**15. Find prime factorization of 85**

**Solution:**

With the factor tree the prime factors are:

The prime factorization of 85 = 5 × 17 = 85

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**5th Grade Math**

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