Use this worksheet to practice breaking down composite numbers into their prime factors.
Prime Factors math worksheet with a table for listing factors and identifying prime numbers.
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Step-by-step solution for: Prime Factorization Worksheets - 15 Worksheets Library
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Step-by-step solution for: Prime Factorization Worksheets - 15 Worksheets Library
Sure! Let’s solve the “Prime Factors” worksheet step by step.
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A prime factor is a prime number that divides another number exactly (with no remainder). Every composite number can be broken down into a product of prime factors — this is called prime factorization.
A prime number is a number greater than 1 that has only two factors: 1 and itself.
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We’ll go row by row and find the prime factorization of each number, then state whether it’s prime or not.
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## ✔ 160 → Already done: `2×2×2×2×2×5` → Not Prime
✔ 59 → Already done: `59` → Prime
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## 🔢 240
Divide by smallest primes:
- 240 ÷ 2 = 120
- 120 ÷ 2 = 60
- 60 ÷ 2 = 30
- 30 ÷ 2 = 15
- 15 ÷ 3 = 5
- 5 ÷ 5 = 1
→ Prime factors: 2 × 2 × 2 × 2 × 3 × 5
→ Not Prime (has more than 2 factors)
---
## 🔢 323
Check divisibility:
- Not even → not divisible by 2
- Sum of digits: 3+2+3=8 → not divisible by 3
- Doesn’t end in 0 or 5 → not divisible by 5
- Try 7: 323 ÷ 7 ≈ 46.14 → no
- Try 11: 323 ÷ 11 ≈ 29.36 → no
- Try 13: 323 ÷ 13 ≈ 24.85 → no
- Try 17: 323 ÷ 17 = 19 → YES!
So: 17 × 19 = 323
Both 17 and 19 are prime → Prime factors: 17 × 19
→ Not Prime
---
## 🔢 360
Divide by 2:
- 360 ÷ 2 = 180
- 180 ÷ 2 = 90
- 90 ÷ 2 = 45
- 45 ÷ 3 = 15
- 15 ÷ 3 = 5
- 5 ÷ 5 = 1
→ Prime factors: 2 × 2 × 2 × 3 × 3 × 5
→ Not Prime
---
## 🔢 313
Check if prime:
- Not even → not divisible by 2
- Sum: 3+1+3=7 → not divisible by 3
- Doesn’t end in 0/5 → not divisible by 5
- Try 7: 313 ÷ 7 ≈ 44.7 → no
- Try 11: 313 ÷ 11 ≈ 28.45 → no
- Try 13: 313 ÷ 13 ≈ 24.07 → no
- Try 17: 313 ÷ 17 ≈ 18.4 → no
- Try 19: 313 ÷ 19 ≈ 16.47 → no
- Try 23: 313 ÷ 23 ≈ 13.6 → no
- Next prime is 29 → 29² = 841 > 313 → we can stop.
✔ 313 is prime
→ Prime factors: 313
→ Prime
---
## 🔢 263
Check if prime:
- Not even → not divisible by 2
- Sum: 2+6+3=11 → not divisible by 3
- Doesn’t end in 0/5 → not divisible by 5
- Try 7: 263 ÷ 7 ≈ 37.57 → no
- Try 11: 263 ÷ 11 ≈ 23.9 → no
- Try 13: 263 ÷ 13 ≈ 20.23 → no
- Try 17: 263 ÷ 17 ≈ 15.47 → no
- Try 19: 263 ÷ 19 ≈ 13.84 → no
- Try 23: 263 ÷ 23 ≈ 11.43 → no
- 29² = 841 > 263 → stop.
✔ 263 is prime
→ Prime factors: 263
→ Prime
---
## 🔢 420
Divide by 2:
- 420 ÷ 2 = 210
- 210 ÷ 2 = 105
- 105 ÷ 3 = 35
- 35 ÷ 5 = 7
- 7 ÷ 7 = 1
→ Prime factors: 2 × 2 × 3 × 5 × 7
→ Not Prime
---
## 🔢 480
Divide by 2:
- 480 ÷ 2 = 240
- 240 ÷ 2 = 120
- 120 ÷ 2 = 60
- 60 ÷ 2 = 30
- 30 ÷ 2 = 15
- 15 ÷ 3 = 5
- 5 ÷ 5 = 1
→ Prime factors: 2 × 2 × 2 × 2 × 2 × 3 × 5
→ Not Prime
---
## 🔢 540
Divide by 2:
- 540 ÷ 2 = 270
- 270 ÷ 2 = 135
- 135 ÷ 3 = 45
- 45 ÷ 3 = 15
- 15 ÷ 3 = 5
- 5 ÷ 5 = 1
→ Prime factors: 2 × 2 × 3 × 3 × 3 × 5
→ Not Prime
---
## 🔢 600
Divide by 2:
- 600 ÷ 2 = 300
- 300 ÷ 2 = 150
- 150 ÷ 2 = 75
- 75 ÷ 3 = 25
- 25 ÷ 5 = 5
- 5 ÷ 5 = 1
→ Prime factors: 2 × 2 × 2 × 3 × 5 × 5
→ Not Prime
---
## 🔢 491
Check if prime:
- Not even → not divisible by 2
- Sum: 4+9+1=14 → not divisible by 3
- Doesn’t end in 0/5 → not divisible by 5
- Try 7: 491 ÷ 7 ≈ 70.14 → no
- Try 11: 491 ÷ 11 ≈ 44.63 → no
- Try 13: 491 ÷ 13 ≈ 37.76 → no
- Try 17: 491 ÷ 17 ≈ 28.88 → no
- Try 19: 491 ÷ 19 ≈ 25.84 → no
- Try 23: 491 ÷ 23 ≈ 21.34 → no
- Try 29: 491 ÷ 29 ≈ 16.93 → no
- Try 31: 491 ÷ 31 ≈ 15.83 → no
- 37² = 1369 > 491 → stop.
✔ 491 is prime
→ Prime factors: 491
→ Prime
---
## 🔢 650
Divide by 2:
- 650 ÷ 2 = 325
- 325 ÷ 5 = 65
- 65 ÷ 5 = 13
- 13 ÷ 13 = 1
→ Prime factors: 2 × 5 × 5 × 13
→ Not Prime
---
## 🔢 720
Divide by 2:
- 720 ÷ 2 = 360
- 360 ÷ 2 = 180
- 180 ÷ 2 = 90
- 90 ÷ 2 = 45
- 45 ÷ 3 = 15
- 15 ÷ 3 = 5
- 5 ÷ 5 = 1
→ Prime factors: 2 × 2 × 2 × 2 × 3 × 3 × 5
→ Not Prime
---
## 🔢 800
Divide by 2:
- 800 ÷ 2 = 400
- 400 ÷ 2 = 200
- 200 ÷ 2 = 100
- 100 ÷ 2 = 50
- 50 ÷ 2 = 25
- 25 ÷ 5 = 5
- 5 ÷ 5 = 1
→ Prime factors: 2 × 2 × 2 × 2 × 2 × 5 × 5
→ Not Prime
---
## ✔ Final Answers Table:
| Number | Prime Factors | Prime? |
|--------|-----------------------------------|------------|
| 160 | 2×2×2×2×2×5 | Not Prime |
| 59 | 59 | Prime |
| 240 | 2×2×2×2×3×5 | Not Prime |
| 323 | 17×19 | Not Prime |
| 360 | 2×2×2×3×3×5 | Not Prime |
| 313 | 313 | Prime |
| 263 | 263 | Prime |
| 420 | 2×2×3×5×7 | Not Prime |
| 480 | 2×2×2×2×2×3×5 | Not Prime |
| 540 | 2×2×3×3×3×5 | Not Prime |
| 600 | 2×2×2×3×5×5 | Not Prime |
| 491 | 491 | Prime |
| 650 | 2×5×5×13 | Not Prime |
| 720 | 2×2×2×2×3×3×5 | Not Prime |
| 800 | 2×2×2×2×2×5×5 | Not Prime |
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✔ You’re all set! This completes the worksheet. Let me know if you want it formatted as a printable answer key.
---
📌 What is a prime factor?
A prime factor is a prime number that divides another number exactly (with no remainder). Every composite number can be broken down into a product of prime factors — this is called prime factorization.
📌 What is a prime number?
A prime number is a number greater than 1 that has only two factors: 1 and itself.
---
We’ll go row by row and find the prime factorization of each number, then state whether it’s prime or not.
---
## ✔ 160 → Already done: `2×2×2×2×2×5` → Not Prime
✔ 59 → Already done: `59` → Prime
---
## 🔢 240
Divide by smallest primes:
- 240 ÷ 2 = 120
- 120 ÷ 2 = 60
- 60 ÷ 2 = 30
- 30 ÷ 2 = 15
- 15 ÷ 3 = 5
- 5 ÷ 5 = 1
→ Prime factors: 2 × 2 × 2 × 2 × 3 × 5
→ Not Prime (has more than 2 factors)
---
## 🔢 323
Check divisibility:
- Not even → not divisible by 2
- Sum of digits: 3+2+3=8 → not divisible by 3
- Doesn’t end in 0 or 5 → not divisible by 5
- Try 7: 323 ÷ 7 ≈ 46.14 → no
- Try 11: 323 ÷ 11 ≈ 29.36 → no
- Try 13: 323 ÷ 13 ≈ 24.85 → no
- Try 17: 323 ÷ 17 = 19 → YES!
So: 17 × 19 = 323
Both 17 and 19 are prime → Prime factors: 17 × 19
→ Not Prime
---
## 🔢 360
Divide by 2:
- 360 ÷ 2 = 180
- 180 ÷ 2 = 90
- 90 ÷ 2 = 45
- 45 ÷ 3 = 15
- 15 ÷ 3 = 5
- 5 ÷ 5 = 1
→ Prime factors: 2 × 2 × 2 × 3 × 3 × 5
→ Not Prime
---
## 🔢 313
Check if prime:
- Not even → not divisible by 2
- Sum: 3+1+3=7 → not divisible by 3
- Doesn’t end in 0/5 → not divisible by 5
- Try 7: 313 ÷ 7 ≈ 44.7 → no
- Try 11: 313 ÷ 11 ≈ 28.45 → no
- Try 13: 313 ÷ 13 ≈ 24.07 → no
- Try 17: 313 ÷ 17 ≈ 18.4 → no
- Try 19: 313 ÷ 19 ≈ 16.47 → no
- Try 23: 313 ÷ 23 ≈ 13.6 → no
- Next prime is 29 → 29² = 841 > 313 → we can stop.
✔ 313 is prime
→ Prime factors: 313
→ Prime
---
## 🔢 263
Check if prime:
- Not even → not divisible by 2
- Sum: 2+6+3=11 → not divisible by 3
- Doesn’t end in 0/5 → not divisible by 5
- Try 7: 263 ÷ 7 ≈ 37.57 → no
- Try 11: 263 ÷ 11 ≈ 23.9 → no
- Try 13: 263 ÷ 13 ≈ 20.23 → no
- Try 17: 263 ÷ 17 ≈ 15.47 → no
- Try 19: 263 ÷ 19 ≈ 13.84 → no
- Try 23: 263 ÷ 23 ≈ 11.43 → no
- 29² = 841 > 263 → stop.
✔ 263 is prime
→ Prime factors: 263
→ Prime
---
## 🔢 420
Divide by 2:
- 420 ÷ 2 = 210
- 210 ÷ 2 = 105
- 105 ÷ 3 = 35
- 35 ÷ 5 = 7
- 7 ÷ 7 = 1
→ Prime factors: 2 × 2 × 3 × 5 × 7
→ Not Prime
---
## 🔢 480
Divide by 2:
- 480 ÷ 2 = 240
- 240 ÷ 2 = 120
- 120 ÷ 2 = 60
- 60 ÷ 2 = 30
- 30 ÷ 2 = 15
- 15 ÷ 3 = 5
- 5 ÷ 5 = 1
→ Prime factors: 2 × 2 × 2 × 2 × 2 × 3 × 5
→ Not Prime
---
## 🔢 540
Divide by 2:
- 540 ÷ 2 = 270
- 270 ÷ 2 = 135
- 135 ÷ 3 = 45
- 45 ÷ 3 = 15
- 15 ÷ 3 = 5
- 5 ÷ 5 = 1
→ Prime factors: 2 × 2 × 3 × 3 × 3 × 5
→ Not Prime
---
## 🔢 600
Divide by 2:
- 600 ÷ 2 = 300
- 300 ÷ 2 = 150
- 150 ÷ 2 = 75
- 75 ÷ 3 = 25
- 25 ÷ 5 = 5
- 5 ÷ 5 = 1
→ Prime factors: 2 × 2 × 2 × 3 × 5 × 5
→ Not Prime
---
## 🔢 491
Check if prime:
- Not even → not divisible by 2
- Sum: 4+9+1=14 → not divisible by 3
- Doesn’t end in 0/5 → not divisible by 5
- Try 7: 491 ÷ 7 ≈ 70.14 → no
- Try 11: 491 ÷ 11 ≈ 44.63 → no
- Try 13: 491 ÷ 13 ≈ 37.76 → no
- Try 17: 491 ÷ 17 ≈ 28.88 → no
- Try 19: 491 ÷ 19 ≈ 25.84 → no
- Try 23: 491 ÷ 23 ≈ 21.34 → no
- Try 29: 491 ÷ 29 ≈ 16.93 → no
- Try 31: 491 ÷ 31 ≈ 15.83 → no
- 37² = 1369 > 491 → stop.
✔ 491 is prime
→ Prime factors: 491
→ Prime
---
## 🔢 650
Divide by 2:
- 650 ÷ 2 = 325
- 325 ÷ 5 = 65
- 65 ÷ 5 = 13
- 13 ÷ 13 = 1
→ Prime factors: 2 × 5 × 5 × 13
→ Not Prime
---
## 🔢 720
Divide by 2:
- 720 ÷ 2 = 360
- 360 ÷ 2 = 180
- 180 ÷ 2 = 90
- 90 ÷ 2 = 45
- 45 ÷ 3 = 15
- 15 ÷ 3 = 5
- 5 ÷ 5 = 1
→ Prime factors: 2 × 2 × 2 × 2 × 3 × 3 × 5
→ Not Prime
---
## 🔢 800
Divide by 2:
- 800 ÷ 2 = 400
- 400 ÷ 2 = 200
- 200 ÷ 2 = 100
- 100 ÷ 2 = 50
- 50 ÷ 2 = 25
- 25 ÷ 5 = 5
- 5 ÷ 5 = 1
→ Prime factors: 2 × 2 × 2 × 2 × 2 × 5 × 5
→ Not Prime
---
## ✔ Final Answers Table:
| Number | Prime Factors | Prime? |
|--------|-----------------------------------|------------|
| 160 | 2×2×2×2×2×5 | Not Prime |
| 59 | 59 | Prime |
| 240 | 2×2×2×2×3×5 | Not Prime |
| 323 | 17×19 | Not Prime |
| 360 | 2×2×2×3×3×5 | Not Prime |
| 313 | 313 | Prime |
| 263 | 263 | Prime |
| 420 | 2×2×3×5×7 | Not Prime |
| 480 | 2×2×2×2×2×3×5 | Not Prime |
| 540 | 2×2×3×3×3×5 | Not Prime |
| 600 | 2×2×2×3×5×5 | Not Prime |
| 491 | 491 | Prime |
| 650 | 2×5×5×13 | Not Prime |
| 720 | 2×2×2×2×3×3×5 | Not Prime |
| 800 | 2×2×2×2×2×5×5 | Not Prime |
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✔ You’re all set! This completes the worksheet. Let me know if you want it formatted as a printable answer key.
Parent Tip: Review the logic above to help your child master the concept of factors and prime numbers worksheet.
