Question

Write the greatest common factor for each of the following terms:
(i) $3x^{2}y,18x{y}^2,$ and $6xy$
(ii) $qrxy,pryz,$ and $rxyz$

Answer 1

(i)
$3x^{2}y=3\times x\times x\times y18x{y}^2=3\times 2\times 3\times x\times y\times y6xy=-1\times 2\times 3\times x\times y$

The greatest common factor is obtained by the product of irreducible common factors in all the terms.

The greatest common factor $=2\times x\times y=2xy$

(ii)
$qrxy=q\times r\times x\times ypryz=p\times r\times y\times zrxyz=r\times x\times y\times z$

The greatest common factor is obtained by the product of irreducible common factors in all the terms.

The greatest common factor $=r\times y=ry$