what is the answer to finding the GCF of m^8n^4 and 3m^6n=
nothing found in the coefficients.
for the m's --- > m^6
for the n's ----> n
so GCF = m^6 n
To find the greatest common factor (GCF) of terms m^8n^4 and 3m^6n, we need to identify the common factors of both terms.
Step 1: Identify the common factors of m^8n^4 and 3m^6n.
The variables m and n are common factors present in both terms. To determine the common factor, we need to find the lowest exponent of each variable in both terms.
For m:
The lowest exponent for m in m^8n^4 is 6 in m^6n.
For n:
The lowest exponent for n in m^8n^4 is 4 in n^4.
Step 2: Determine the common factor.
The common factor for m is m^6, and for n, it is n^4.
Step 3: Multiply the common factors.
The GCF of m^8n^4 and 3m^6n is obtained by multiplying the common factors:
GCF = m^6 * n^4.
Therefore, the GCF of m^8n^4 and 3m^6n is m^6n^4.
To find the greatest common factor (GCF) of the given terms, follow these steps:
Step 1: Identify the common factors of the numerical coefficients (numbers).
In this case, the numerical coefficients are 1 and 3. There are no other common factors besides 1, so the GCF of the numerical coefficients is 1.
Step 2: Identify the common factors of the variables (letters) and their exponents.
The variables in this case are m and n. Let's examine the exponents of each variable:
m^8n^4 and 3m^6n
For m, the exponents are 8 and 6, respectively. The common factor for m is m^6 since it is the smaller exponent.
For n, the exponents are 4 and 1, respectively. The common factor for n is n^1 since it is the smaller exponent.
Step 3: Combine the common factors identified in Steps 1 and 2.
The GCF of m^8n^4 and 3m^6n is the product of the common factors of the numerical coefficients and variables:
GCF = 1 * m^6 * n^1 = m^6n
Therefore, the GCF of m^8n^4 and 3m^6n is m^6n.