Prime Factorization worksheet

1. Prime factorization of 325: 5² × 13

1. Divide by the smallest prime that goes in evenly. Then repeat with the answer until only 1 or a prime is left

   $\text{325 → ÷ 2, 3, 5, 7, 11, …}$

2. The prime 5 goes into 325 evenly, so divide it out

   $\frac{325}{5}$$=65$

3. The prime 5 goes into 65 evenly, so divide it out

   $\frac{65}{5}$$=13$

4. No prime up to √13 ≈ 3.61 divides 13, so the last number left is prime itself

   $\text{last factor}$$=13$

5. Gather the primes you divided by. Write each repeated prime as a power to keep it short

   $325$$=5^2\times 13$

6. That gives the prime factorization

   $325$$=\text{5² × 13}$

2. Prime factorization of 400: 2⁴ × 5²

1. Divide by the smallest prime that goes in evenly. Then repeat with the answer until only 1 or a prime is left

   $\text{400 → ÷ 2, 3, 5, 7, 11, …}$

2. The prime 2 goes into 400 evenly, so divide it out

   $\frac{400}{2}$$=200$

3. The prime 2 goes into 200 evenly, so divide it out

   $\frac{200}{2}$$=100$

4. The prime 2 goes into 100 evenly, so divide it out

   $\frac{100}{2}$$=50$

5. The prime 2 goes into 50 evenly, so divide it out

   $\frac{50}{2}$$=25$

6. The prime 5 goes into 25 evenly, so divide it out

   $\frac{25}{5}$$=5$

7. The prime 5 goes into 5 evenly, so divide it out

   $\frac{5}{5}$$=1$

8. Gather the primes you divided by. Write each repeated prime as a power to keep it short

   $400$$=2^4\times 5^2$

9. That gives the prime factorization

   $400$$=\text{2⁴ × 5²}$

3. Prime factorization of 425: 5² × 17

1. Divide by the smallest prime that goes in evenly. Then repeat with the answer until only 1 or a prime is left

   $\text{425 → ÷ 2, 3, 5, 7, 11, …}$

2. The prime 5 goes into 425 evenly, so divide it out

   $\frac{425}{5}$$=85$

3. The prime 5 goes into 85 evenly, so divide it out

   $\frac{85}{5}$$=17$

4. No prime up to √17 ≈ 4.12 divides 17, so the last number left is prime itself

   $\text{last factor}$$=17$

5. Gather the primes you divided by. Write each repeated prime as a power to keep it short

   $425$$=5^2\times 17$

6. That gives the prime factorization

   $425$$=\text{5² × 17}$

4. Prime factorization of 270: 2 × 3³ × 5

1. Divide by the smallest prime that goes in evenly. Then repeat with the answer until only 1 or a prime is left

   $\text{270 → ÷ 2, 3, 5, 7, 11, …}$

2. The prime 2 goes into 270 evenly, so divide it out

   $\frac{270}{2}$$=135$

3. The prime 3 goes into 135 evenly, so divide it out

   $\frac{135}{3}$$=45$

4. The prime 3 goes into 45 evenly, so divide it out

   $\frac{45}{3}$$=15$

5. The prime 3 goes into 15 evenly, so divide it out

   $\frac{15}{3}$$=5$

6. No prime up to √5 ≈ 2.24 divides 5, so the last number left is prime itself

   $\text{last factor}$$=5$

7. Gather the primes you divided by. Write each repeated prime as a power to keep it short

   $270$$=2\times 3^3\times 5$

8. That gives the prime factorization

   $270$$=\text{2 × 3³ × 5}$

5. Prime factorization of 300: 2² × 3 × 5²

1. Divide by the smallest prime that goes in evenly. Then repeat with the answer until only 1 or a prime is left

   $\text{300 → ÷ 2, 3, 5, 7, 11, …}$

2. The prime 2 goes into 300 evenly, so divide it out

   $\frac{300}{2}$$=150$

3. The prime 2 goes into 150 evenly, so divide it out

   $\frac{150}{2}$$=75$

4. The prime 3 goes into 75 evenly, so divide it out

   $\frac{75}{3}$$=25$

5. The prime 5 goes into 25 evenly, so divide it out

   $\frac{25}{5}$$=5$

6. The prime 5 goes into 5 evenly, so divide it out

   $\frac{5}{5}$$=1$

7. Gather the primes you divided by. Write each repeated prime as a power to keep it short

   $300$$=2^2\times 3\times 5^2$

8. That gives the prime factorization

   $300$$=\text{2² × 3 × 5²}$

6. Prime factorization of 240: 2⁴ × 3 × 5

1. Divide by the smallest prime that goes in evenly. Then repeat with the answer until only 1 or a prime is left

   $\text{240 → ÷ 2, 3, 5, 7, 11, …}$

2. The prime 2 goes into 240 evenly, so divide it out

   $\frac{240}{2}$$=120$

3. The prime 2 goes into 120 evenly, so divide it out

   $\frac{120}{2}$$=60$

4. The prime 2 goes into 60 evenly, so divide it out

   $\frac{60}{2}$$=30$

5. The prime 2 goes into 30 evenly, so divide it out

   $\frac{30}{2}$$=15$

6. The prime 3 goes into 15 evenly, so divide it out

   $\frac{15}{3}$$=5$

7. No prime up to √5 ≈ 2.24 divides 5, so the last number left is prime itself

   $\text{last factor}$$=5$

8. Gather the primes you divided by. Write each repeated prime as a power to keep it short

   $240$$=2^4\times 3\times 5$

9. That gives the prime factorization

   $240$$=\text{2⁴ × 3 × 5}$

7. Prime factorization of 390: 2 × 3 × 5 × 13

1. Divide by the smallest prime that goes in evenly. Then repeat with the answer until only 1 or a prime is left

   $\text{390 → ÷ 2, 3, 5, 7, 11, …}$

2. The prime 2 goes into 390 evenly, so divide it out

   $\frac{390}{2}$$=195$

3. The prime 3 goes into 195 evenly, so divide it out

   $\frac{195}{3}$$=65$

4. The prime 5 goes into 65 evenly, so divide it out

   $\frac{65}{5}$$=13$

5. No prime up to √13 ≈ 3.61 divides 13, so the last number left is prime itself

   $\text{last factor}$$=13$

6. Gather the primes you divided by. Write each repeated prime as a power to keep it short

   $390$$=2\times 3\times 5\times 13$

7. That gives the prime factorization

   $390$$=\text{2 × 3 × 5 × 13}$

8. Prime factorization of 420: 2² × 3 × 5 × 7

1. Divide by the smallest prime that goes in evenly. Then repeat with the answer until only 1 or a prime is left

   $\text{420 → ÷ 2, 3, 5, 7, 11, …}$

2. The prime 2 goes into 420 evenly, so divide it out

   $\frac{420}{2}$$=210$

3. The prime 2 goes into 210 evenly, so divide it out

   $\frac{210}{2}$$=105$

4. The prime 3 goes into 105 evenly, so divide it out

   $\frac{105}{3}$$=35$

5. The prime 5 goes into 35 evenly, so divide it out

   $\frac{35}{5}$$=7$

6. The prime 7 goes into 7 evenly, so divide it out

   $\frac{7}{7}$$=1$

7. Gather the primes you divided by. Write each repeated prime as a power to keep it short

   $420$$=2^2\times 3\times 5\times 7$

8. That gives the prime factorization

   $420$$=\text{2² × 3 × 5 × 7}$

9. Prime factorization of 320: 2⁶ × 5

1. Divide by the smallest prime that goes in evenly. Then repeat with the answer until only 1 or a prime is left

   $\text{320 → ÷ 2, 3, 5, 7, 11, …}$

2. The prime 2 goes into 320 evenly, so divide it out

   $\frac{320}{2}$$=160$

3. The prime 2 goes into 160 evenly, so divide it out

   $\frac{160}{2}$$=80$

4. The prime 2 goes into 80 evenly, so divide it out

   $\frac{80}{2}$$=40$

5. The prime 2 goes into 40 evenly, so divide it out

   $\frac{40}{2}$$=20$

6. The prime 2 goes into 20 evenly, so divide it out

   $\frac{20}{2}$$=10$

7. The prime 2 goes into 10 evenly, so divide it out

   $\frac{10}{2}$$=5$

8. No prime up to √5 ≈ 2.24 divides 5, so the last number left is prime itself

   $\text{last factor}$$=5$

9. Gather the primes you divided by. Write each repeated prime as a power to keep it short

   $320$$=2^6\times 5$

10. That gives the prime factorization

    $320$$=\text{2⁶ × 5}$

10. Prime factorization of 275: 5² × 11

1. Divide by the smallest prime that goes in evenly. Then repeat with the answer until only 1 or a prime is left

   $\text{275 → ÷ 2, 3, 5, 7, 11, …}$

2. The prime 5 goes into 275 evenly, so divide it out

   $\frac{275}{5}$$=55$

3. The prime 5 goes into 55 evenly, so divide it out

   $\frac{55}{5}$$=11$

4. No prime up to √11 ≈ 3.32 divides 11, so the last number left is prime itself

   $\text{last factor}$$=11$

5. Gather the primes you divided by. Write each repeated prime as a power to keep it short

   $275$$=5^2\times 11$

6. That gives the prime factorization

   $275$$=\text{5² × 11}$