write 28 + 24 as a product of two factors using the GCF and the distributive property
The Correct Answer and Explanation is:
Correct Answer:
We are asked to write 28 + 24 as a product of two factors using the GCF (Greatest Common Factor) and the distributive property.
Step 1: Find the GCF of 28 and 24
- Factors of 28: 1, 2, 4, 7, 14, 28
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Common Factors: 1, 2, 4
- GCF: 4
Step 2: Use the Distributive Property
Write each term as a product with the GCF:
- 28 = 4 × 7
- 24 = 4 × 6
So,
28 + 24 = 4 × 7 + 4 × 6
Now factor out the common factor (4):
28 + 24 = 4(7 + 6)
28 + 24 = 4 × 13
Final Answer:
28 + 24 = 4 × 13
Explanation:
To express a sum like 28 + 24 as a product of two factors, we use the Greatest Common Factor (GCF) and the distributive property. This technique is useful in simplifying expressions and understanding factorization.
First, determine the GCF of 28 and 24. A common factor is a number that divides both numbers exactly. For 28, the factors are 1, 2, 4, 7, 14, and 28. For 24, they are 1, 2, 3, 4, 6, 8, 12, and 24. The largest number both lists share is 4, so the GCF is 4.
Next, rewrite each number as a product using the GCF:
- 28 = 4 × 7
- 24 = 4 × 6
Then apply the distributive property in reverse. This property says that a(b + c) = ab + ac. So in reverse, we take:
4 × 7 + 4 × 6 = 4(7 + 6)
This gives:
4(13) = 52, which is the same as 28 + 24.
So, 28 + 24 = 4 × 13.
This process shows how to factor out the GCF and turn a sum into a product. It’s especially helpful in algebra, where factoring expressions is a key skill. This not only simplifies calculations but also builds a strong foundation for solving equations and working with polynomials.
