Write an equivalent expression by taking out the greatest common factor.
32c + 16d =16 (2,1)
I have problem check this for me
so divide everything by 16
To find the greatest common factor (GCF) of 32c and 16d, we need to break down each term into its prime factors.
For 32c:
Prime factorization of 32 = 2^5
So, 32c = 2^5 * c
For 16d:
Prime factorization of 16 = 2^4
So, 16d = 2^4 * d
The GCF of 32c and 16d is the common factors they share, which is 2^4.
Now, to write an equivalent expression by taking out the greatest common factor, we divide each term by the GCF.
32c / (2^4) = 2 * (2^1 * c) = 2(2c)
16d / (2^4) = 1 * (2^1 * d) = 2d
The equivalent expression, after taking out the GCF, is:
2(2c) + 2d = 16
To find the greatest common factor (GCF) of 32c and 16d, we need to determine the largest number that divides evenly into both terms.
First, let's look at the coefficients. The factors of 32 are 1, 2, 4, 8, 16, and 32. The factors of 16 are 1, 2, 4, 8, and 16. The largest number that is common to both lists is 16. So, the GCF of 32c and 16d is 16.
To take out the GCF from the expression 32c + 16d, we divide each term by 16:
32c ÷ 16 = 2c
16d ÷ 16 = d
Now, we can rewrite the equation as:
2c + d = 16
Therefore, the equivalent expression, after taking out the greatest common factor, is 2c + d = 16.