The greatest common factor (GCF) of the algebraic expressions m⁷n⁴p³ and mn¹²p⁵ is mn⁴p³.
What is the greatest common factor (GCF) of two or more algebraic expressions?
The largest expression that is a factor of all the expressions is known as the greatest common factor (GCF) of two or more expressions.
The steps we take to determine the greatest common factor are summarized as follows:-
- Divide every coefficient by a prime. Expand the form of all variables using exponents.
- Add a column for each factor that matches a common factor. Mark the common elements in each column.
- Reduce the components that all expressions have in common.
- Multiply the factors.
How to solve the question?
In the question, we are asked to find the GCF of the algebraic expressions m⁷n⁴p³ and mn¹²p⁵.
To find the GCF, we follow the steps discussed above.
- Expand the form of the variables using the exponents, thus, m⁷n⁴p³ = m.m.m.m.m.m.m.n.n.n.n.p.p.p, and mn¹²p⁵ = m.n.n.n.n.n.n.n.n.n.n.n.n.p.p.p.p.p.
- Add columns for each factor, by taking common elements, thus, for m we get m, for n we get n.n.n.n, and for p we get p.p.p.
- Reduce each factor, thus, we m for m, n⁴ for n, and p³ for p.
- Multiply all the factors, thus, we get mn⁴p³.
Thus, the greatest common factor (GCF) of the algebraic expressions m⁷n⁴p³ and mn¹²p⁵ is mn⁴p³.
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