Highest Common Factor of Monomials

How to find the highest common factor of monomials?

To find the highest common factor (H.C.F.) or greatest common factor (G.C.F.) of two or more monomials is the product of the H.C.F. of their numerical coefficients and the H.C.F. of their literal coefficients.

Note: Note: The H.C.F. of literal coefficients is each common literal with the lowest power.

Solved examples to find highest common factor of monomials:

1. Find the H.C.F. of 4x²y³ and 6xy²z.

Solution:

The H.C.F. of numerical coefficients = The H.C.F. of 4 and 6.

Since, 4 = 2 × 2 = 2² and 6 = 2 × 3 = 2¹ × 3¹

Therefore, the H.C.F. of 4 and 6 is 2


The H.C.F. of literal coefficients = The H.C.F. of x²y³ and xy²z = xy²

Since, in x²y³ and xy²z, x and y are common.

The lowest power of x is x.

The lowest power of y is y².

Therefore, the H.C.F. of x²y³ and xy²z is xy².

Thus, the H.C.F. of 4x²y³ and 6xy²z

= The H.C.F. of numerical coefficients × The H.C.F. of literal coefficients

= 2 × (xy²)

= 2xy².



2. Find the H.C.F. of 8a³b²c and 12abc².

Solution:

The H.C.F. of numerical coefficients = The H.C.F. of 8 and 12.

Since, 8 = 2 × 2 × 2 = 2³ and 12 = 2 × 2 × 3 = 2² × 3¹

Therefore, the H.C.F. of 8 and 12 is 4

The H.C.F. of literal coefficients = The H.C.F. of a³b²c and abc² = abc

Since, in a³b²c and abc², a, b and c are common.

The lowest power of a is a.

The lowest power of b is b.

The lowest power of c is c.

Therefore, the H.C.F. of a³b²c and abc² is abc.

Thus, the H.C.F. of 8a³b²c and 12abc²

= The H.C.F. of numerical coefficients × The H.C.F. of literal coefficients

= 4 × (abc)

= 4abc.

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8th Grade Math Practice

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