Highest Common Factor (H.C.F) of Monomials

The H.C.F of given monomials is the common factor having greatest coefficient and highest powers of the variables.

Ex: 1) Find H.C.F of $6x^{3}y$ and $18x^{2}y^{3}$.

Sol: $6x^{3}y = 2 \times 3 \times x^{3} \times y$

$\quad \quad \ 18x^{2}y^{3} = 2 \times 3^{2} \times x^{2} \times y^{3}$

$\quad \quad \ \text{H.C.F} = 2 \times 3 \times x^{2} \times y$

$\quad \quad \quad \quad \quad \quad \ = 6x^{2}y$

Ex: 2) Find H.C.F of $5xy$ and $10x$.

Sol: $5xy = 5 \times x \times y$

$\quad \quad \ 10x = 2 \times 5 \times x$

$\quad \quad \ \text{H.C.F} = 5x$

Ex: 3) H.C.F of $12a^{2}b$ and $15ab^{2}$ is 3ab

Ex: 4) H.C.F of $2x$ and $4$ is 2

Ex: 5) H.C.F of $12x$ and $36$ is 12

Ex: 6) H.C.F of $14pq$ and $35pqr$ is 7pq