Question

which of the following is the common factor of 21 x y and 35 x y2​

Answer 1

Answer:

Find the greatest common factor (GCF/HCF) of the following polynomials: (1-14)

1. 2x2 and 12x2

Solution:

We know that the numerical coefficients of given numerical are 2 and 12

The greatest common factor of 2 and 12 is 2

The common literals appearing in given monomial is x

The smallest power of x in two monomials is 2

The monomial of common literals with smallest power is x2

∴ The greatest common factor = 2x2

2. 6x3y and 18x2y3

Solution:

We know that the numerical coefficients of given numerical are 6 and18

The greatest common factor of 6 and 18 is 6

Common literals appearing in given numerical are x and y

Smallest power of x in three monomial is 2

Smallest power of y in three monomial is 1

Monomial of common literals with smallest power is x2y

∴ The greatest common factor = 6x2y

3. 7x, 21x2 and 14xy2

Solution:

We know that the numerical coefficients of given numerical are 7, 21 and 14

Greatest common factor of 7, 21 and 14 is 7

Common literals appearing in given numerical are x and y

Smallest power of x in three monomials is 1

Smallest power of y in three monomials is 0

Monomials of common literals with smallest power is x

∴ The greatest common factor = 7x

4. 42x2yz and 63x3y2z3

Solution:

We know that the numerical coefficients of given numerical are 42 and 63.

Greatest common factor of 42, 63 is 21.

Common literals appearing in given numerical are x, y and z

Smallest power of x in two monomials is 2

Smallest power of y in two monomials is 1

Smallest power of z in two monomials is 1

Monomials of common literals with smallest power is x2yz

∴ The greatest common factor = 21x2yz

5. 12ax2, 6a2x3 and 2a3x5

Solution:

We know that the numerical coefficients of given numerical are 12, 6 and 2

Greatest common factor of 12, 6 and 2 is 2.

Common literals appearing in given numerical are a and x

Smallest power of x in three monomials is 2

Smallest power of a in three monomials is 1

Monomials of common literals with smallest power is ax2

∴ The greatest common factor = 2ax2

6. 9x2, 15x2y3, 6xy2 and 21x2y2

Solution:

We know that the numerical coefficients of given numerical are 9, 15, 16 and 21

Greatest common factor of 9, 15, 16 and 21 is 3.

Common literals appearing in given numerical are x and y

Smallest power of x in four monomials is 1

Smallest power of y in four monomials is 0

Monomials of common literals with smallest power is x

∴ The greatest common factor