We are using the factorization method to calculate the highest common factor of monomials. Factorization is the process of breaking an entity into a product of another entity which when multiplied together gives the original entity. Get the example questions on finding the greatest common factor or Highest Common Factor of Monomials by Factorization.

HCF of Monomials Solved Examples

Example 1.

Find the H.C.F. of the monomials 16x²y³and 22x²y.

Solution:

The H.C.F. of numerical coefficients = The H.C.F. of 16, 22

Since, 16 = 2 * 2 * 2 * 2, 22 = 2 * 11

Therefore, the H.C.F. of 16, 22 is 2.

Now, the variables x and y are present in all the quantities. Out of these the highest common power of x is 2 and the highest common power if y is 1.

Therefore, the required H.C.F. = 2x²y¹ = 2x²y

The method by which the Highest common factor of the monomials is determined can be formulated as follows:

(i) The G.C.F. of the numerical coefficients are to be determined at first.

(ii) Then the variables are to be written beside the coefficient with their greatest common power or highest common power.

Example 2.

Find the Greatest Common Factor of the monomials 90x⁴y²z³, 54x²y³z⁴, and 18x³y²z³.

Solution:

The H.C.F. of numerical coefficients = The H.C.F. of 90, 54, and 18

Since, 90 = 2 * 5 * 9, 54 = 2 * 3 * 9, 18 = 2 * 9

Therefore, the H.C.F. of 90, 54, and 18 is 2 * 9 = 18.

Now, the variables x, y, and z are available in all the quantities. The highest common power of x is 2, the highest common power of y is 2, and the greatest common power of z is 3.

Therefore, the required greatest common factor = 18x²y²z³

Example 3.

Find the G.C.F of 20abc, 22a²b²c², and 24a³b³c².

Solution:

20abc = 2 * 2 * 5 * a * b * c

22a²b²c² = 2 * 11 * a * a * b * b * c * c

24a³b³c² = 2 * 2 * 2 * 3 * a * a * a * b * b * b * c * c

From the resolved factors of the above three monomials, the common factors are 2, a, b, c

Therefore, the required H.C.F. = 2 * a * b * c = 2abc