Find the GCF of 42m-28n
To find the greatest common factor (GCF) of 42m-28n, we need to identify the common factors of both terms and find the greatest one.
First, let's factor out the greatest common factor from each term:
42m = 2 * 3 * 7 * m
28n = 2 * 2 * 7 * n
The common factors are 2, 7, and m. Since we're looking for the greatest common factor, we can multiply these common factors together:
GCF = 2 * 7 * m = 14m
Therefore, the GCF of 42m-28n is 14m.
To find the greatest common factor (GCF) of 42m and 28n, we need to find the largest number or expression that divides evenly into both 42m and 28n.
Step 1: Prime factorize both numbers.
42m = 2 * 3 * 7 * m
28n = 2 * 2 * 7 * n
Step 2: Identify the common factors.
The common factors are 2 and 7.
Step 3: Choose the smallest exponent for each common factor.
From the prime factorization above, we can see that the exponent of 2 is 1 in both numbers, and the exponent of 7 is also 1 in both numbers.
Step 4: Multiply the common factors with the smallest exponent.
The GCF of 42m and 28n is 2 * 7 = 14.
Therefore, the GCF of 42m and 28n is 14.
To find the greatest common factor (GCF) of 42m and -28n, we need to first factorize both expressions into their prime factors.
First, let's factorize 42m:
42 can be divided by 2:
42 = 2 * 21
21 can be divided by 3:
21 = 3 * 7
So, 42m can be written as (2 * 3 * 7) * m, or 6 * 7m.
Now, let's factorize -28n:
-28 can be divided by 2:
-28 = 2 * -14
-14 can be divided by 2:
-14 = 2 * -7
So, -28n can be written as (2 * 2 * -7) * n, or -4 * 7n.
From the factorization above, we can see that both 42m and -28n have a factor of 2 and a factor of 7. However, we should consider the exponent of each factor in order to find the GCF.
The GCF is the product of the lowest exponent of each common prime factor.
For the factor 2, the lowest exponent is 1 (from 6 * 7m) because -4 * 7n doesn't have a factor of 2 raised to the power of 2.
For the factor 7, the lowest exponent is 1 (from 6 * 7m) because -4 * 7n doesn't have a factor of 7 raised to any power.
Therefore, the GCF of 42m and -28n is 2 * 7, which is 14.