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:

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

Since, 4 = 2 × 2 = 2

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

The H.C.F. of literal coefficients = The H.C.F. of x

Since, in x

The lowest power of x is x.

The lowest power of y is y

Therefore, the H.C.F. of x

Thus, the H.C.F. of 4x

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

= 2 × (xy

= 2xy

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

Since, 8 = 2 × 2 × 2 = 2

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

The H.C.F. of literal coefficients = The H.C.F. of a

Since, in a

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 a

Thus, the H.C.F. of 8a

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

= 4 × (abc)

= 4abc.

**8th Grade Math Practice**

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