Factor 48y + 26z using the GCF.
Options:
12(4y + 3z)
4(12y + 9z)
16(3y + 2z)
6(8y + 6z)
To factor 48y + 26z using the GCF, we need to find the greatest common factor of 48y and 26z.
The prime factorization of 48y is 2 * 2 * 2 * 2 * 3 * y = 2^4 * 3 * y
The prime factorization of 26z is 2 * 13 * z
The common factors are 2 and z.
Therefore, the GCF is 2z.
To factor out the GCF, we divide each term of 48y + 26z by 2z:
48y / 2z = 24y/z = 24yz/z = 24y
26z / 2z = 13
So, the factored form of 48y + 26z using the GCF is 2z(24y + 13).
None of the given options matches this factored form, so none of the options is correct.
Try again
Apologies for the incorrect response. Let's try factoring 48y + 26z using the GCF correctly.
The GCF of 48 and 26 is 2.
When we factor out 2 from each term, we get:
48y + 26z = 2(24y + 13z)
Therefore, the correct option is 2(24y + 13z).
Pick out of my options the correct answer
The correct option out of the given options is:
4(12y + 9z)
To factor the expression 48y + 26z using the Greatest Common Factor (GCF), we need to find the largest number that can divide both 48y and 26z evenly.
Step 1: Find the GCF of the coefficients 48 and 26.
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
The factors of 26 are 1, 2, 13, 26.
The largest number that divides both 48 and 26 evenly is 2.
Step 2: Divide each term by the GCF, which is 2.
48y ÷ 2 = 24y
26z ÷ 2 = 13z
Step 3: Rewrite the expression using the factored GCF.
48y + 26z = 2(24y + 13z)
Therefore, the correct factorization of 48y + 26z using the GCF is 2(24y + 13z).
Among the given options, the correct one is 2(24y + 13z), so the answer is: 2(24y + 13z).