Question

A trade has 612 dettol soaps and 342 pear soaps. he packs them in boxes and each box contains exactly one type of soap. If every box contains the same number of soaps, then find the number of soaps in each box such that the number of boxes is the least.

Answer 1

The required number is HCF of 612 and 342.

This gives the maximum number of soaps in each box and the number of boxes with them be the least.

By using Euclid's division algorithm, we have

$612=342\times 1+270$

$342=270\times 1+72$

$270=72\times 3+54$

$72=54\times 1+18$

$54=18\times 3+0$

Here we notice that the remainder is zero, and the divisor at this stage is 18.

Therefore. HCF of 612 and 342 is 18.

So, the trader can pack 18 soaps per box.