Find the GCF of 42m−28n.(1 point)
Responses
7
7
2
2
84
84
14
14
To find the greatest common factor (GCF) of 42m - 28n, we need to factor out the common factors from the two terms.
Step 1: Factor out the common factor from the numbers 42 and 28:
42 = 2 × 3 × 7
28 = 2 × 2 × 7
Step 2: Find the common factors in the expressions m and n.
Since m and n have no common factors, we can't factor out anything.
Step 3: Combine the common factors from both the numbers and the variables:
GCF = 2 × 7 = 14
Therefore, the GCF of 42m - 28n is 14.
To find the Greatest Common Factor (GCF) of 42m-28n, we need to find the largest number that divides evenly into both 42m and 28n.
Step 1: Factorize both numbers.
42m can be factored as 2 * 3 * 7 * m.
28n can be factored as 2 * 2 * 7 * n.
Step 2: Identify the common factors.
The common factors between 42m and 28n are 2, 7.
Step 3: Determine the lowest exponent.
Since the common factor 2 appears twice in the factorization of 28n, and only once in the factorization of 42m, we take the lowest exponent, which is 1.
Step 4: Multiply the common factors with the lowest exponent.
GCF = 2^1 * 7^1 = 2 * 7 = 14.
Therefore, the GCF of 42m - 28n is 14.