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 4x
^{2}y
^{3} and 6xy
^{2}z.
Solution:
The H.C.F. of numerical coefficients = The H.C.F. of 4 and 6.
Since, 4 = 2 × 2 = 2
^{2} and 6 = 2 × 3 = 2
^{1} × 3
^{1}
Therefore, the H.C.F. of 4 and 6 is 2
The H.C.F. of literal coefficients = The H.C.F. of x
^{2}y
^{3} and xy
^{2}z = xy
^{2}
Since, in x
^{2}y
^{3} and xy
^{2}z, x and y are common.
The lowest power of x is x.
The lowest power of y is y
^{2}.
Therefore, the H.C.F. of x
^{2}y
^{3} and xy
^{2}z is xy
^{2}.
Thus, the H.C.F. of 4x
^{2}y
^{3} and 6xy
^{2}z
= The H.C.F. of numerical coefficients × The H.C.F. of literal coefficients
= 2 × (xy
^{2})
= 2xy
^{2}.
2. Find the H.C.F. of 8a
^{3}b
^{2}c and 12abc
^{2}.
Solution:
The H.C.F. of numerical coefficients = The H.C.F. of 8 and 12.
Since, 8 = 2 × 2 × 2 = 2
^{3} and 12 = 2 × 2 × 3 = 2
^{2} × 3
^{1}
Therefore, the H.C.F. of 8 and 12 is 4
The H.C.F. of literal coefficients = The H.C.F. of a
^{3}b
^{2}c and abc
^{2} = abc
Since, in a
^{3}b
^{2}c and abc
^{2}, 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 a
^{3}b
^{2}c and abc
^{2} is abc.
Thus, the H.C.F. of 8a
^{3}b
^{2}c and 12abc
^{2}
= 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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