# 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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