How do you find the GCF (greatest common factor) of -m^8n^4 and 3m^6n?
m^6n
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To find the greatest common factor (GCF) of -m^8n^4 and 3m^6n, we can break down each term into its prime factors and then identify the common factors.
First, let's break down the terms into their prime factors:
-m^8n^4 = -1 * (m * m * m * m * m * m * m * m) * (n * n * n * n)
3m^6n = 3 * (m * m * m * m * m * m) * n
Next, we can identify the common factors by choosing the minimum exponent for each prime factor that appears in both terms:
Common factors:
m^6
n^1
Finally, we multiply the common factors to find the GCF:
GCF = m^6 * n^1 = m^6n
To find the greatest common factor (GCF) of two or more terms, we need to break down each term into its prime factors and determine the common factors.
Let's work through the problem step by step:
1. Start by writing each term in factor form:
-m^8n^4 can be expressed as (-1) * (m * m * m * m * m * m * m * m) * (n * n * n * n)
3m^6n can be expressed as 3 * (m * m * m * m * m * m) * n
2. Identify the common factors. In this case, the common factors are -1, m^6, and n:
-m^8n^4 = (-1) * (m^6) * (m^2) * (n^4)
3m^6n = 3 * (m^6) * n
3. The GCF is obtained by multiplying the common factors together. In this case, the GCF is (-1) * m^6 * n, which simplifies to -m^6n.
Therefore, the GCF of -m^8n^4 and 3m^6n is -m^6n.