Write 32 +24 as a product of two factors using the gcf and the distributive property
The correct answer and explanation is:
To express 32+2432 + 24 as a product of two factors using the greatest common factor (GCF) and the distributive property, we begin by identifying the GCF of 32 and 24.
Step 1: Find the GCF of 32 and 24
The GCF is the largest number that divides both 32 and 24 without leaving a remainder. To find it, list the factors of each number:
- Factors of 32: 1, 2, 4, 8, 16, 32
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
The greatest common factor is 8, since 8 is the largest number that appears in both lists.
Step 2: Factor out the GCF
Now that we know the GCF is 8, we can factor both 32 and 24 by dividing each number by 8: 32=8×432 = 8 \times 4 24=8×324 = 8 \times 3
Thus, we can rewrite the original expression 32+2432 + 24 as: 32+24=(8×4)+(8×3)32 + 24 = (8 \times 4) + (8 \times 3)
Step 3: Apply the distributive property
The distributive property states that a(b+c)=ab+aca(b + c) = ab + ac. In this case, we can factor out the 8: 32+24=8×(4+3)32 + 24 = 8 \times (4 + 3)
Step 4: Simplify the expression
Now, simplify inside the parentheses: 4+3=74 + 3 = 7
Thus, the expression becomes: 32+24=8×732 + 24 = 8 \times 7
Conclusion
The sum of 32 and 24 can be written as the product of two factors, 8×78 \times 7. This is the factorization using the GCF and the distributive property. The distributive property allows us to rewrite the sum as a multiplication, which can be useful in simplifying expressions and solving problems efficiently.