Let's solve the problem step by step based on the worksheet you've provided.
---
Understanding the Concept: Greatest Common Factor (GCF)
The
Greatest Common Factor (GCF) is the largest number that divides two or more numbers without leaving a remainder. To find it, we:
1.
Find the prime factorization of each number.
2.
Identify the common prime factors.
3.
Multiply the common prime factors to get the GCF.
---
Now let’s go through each part of the worksheet and fill in the blanks.
---
Part 1: Circle the common prime factors
####
1. 4 = 2 × 2
6 = 2 × 3
- Common prime factor:
2
- The GCF is:
2
✔ Answer:
- Common prime factor:
2
- GCF:
2
---
####
2. 6 = 2 × 3
9 = 3 × 3
- Common prime factor:
3
- The GCF is:
3
✔ Answer:
- Common prime factor:
3
- GCF:
3
---
####
3. 10 = 2 × 5
12 = 2 × 2 × 3
- Common prime factor:
2
- The GCF is:
2
✔ Answer:
- Common prime factor:
2
- GCF:
2
---
####
4. 14 = 2 × 7
35 = 5 × 7
- Common prime factor:
7
- The GCF is:
7
✔ Answer:
- Common prime factor:
7
- GCF:
7
---
Part 2: Use multiplication of common factors
####
5. 18 = 2 × 3 × 3
12 = 2 × 2 × 3
- Common prime factors:
2 and 3
- Multiply them:
2 × 3 = 6
- The GCF is:
6
✔ Answer:
- Common prime factors:
2 and 3
- GCF:
6
---
####
6. 20 = 2 × 2 × 5
30 = 2 × 3 × 5
- Common prime factors:
2 and 5
- Multiply them:
2 × 5 = 10
- The GCF is:
10
✔ Answer:
- Common prime factors:
2 and 5
- GCF:
10
---
✔ Final Answers Summary:
| Pair | Common Prime Factors | GCF |
|------|------------------------|-----|
| 4 & 6 | 2 | 2 |
| 6 & 9 | 3 | 3 |
| 10 & 12 | 2 | 2 |
| 14 & 35 | 7 | 7 |
| 18 & 12 | 2, 3 | 6 |
| 20 & 30 | 2, 5 | 10 |
---
🔍 Explanation Recap:
- We break down each number into its
prime factors.
- Then, we look for
shared prime factors between the two numbers.
- Multiply those shared factors to get the
GCF.
- If there are no common factors other than 1, then the GCF is
1.
This method works efficiently and helps avoid guessing — it's systematic!
Let me know if you'd like this turned into a printable answer sheet!
Parent Tip: Review the logic above to help your child master the concept of greatest common factor worksheets.
