Find the largest size of squares that can pave a given rectangle

Question

The floor of a hall 252cm long, 162cm wide is paved with equal squares. Find the largest size of marble and number required, if only whole marbles are used.

See the attempted solution posted as an answer.

Answer 1

I tried it out, here's what I got.....

GCF of (252 &162). = 2^2*3^2*7. &. 2*3^4. = 2*3^2. =18. (number of marbles required). largest size of marble = 252/18. & 162/18. =14 & 9. (largest marble is 14cm long & 9cm wide).

Answer 2

You have stated in your title exactly what needs to be done: find the GCF (greatest common factor) of 252 and 162. Some peopel refer to this as the GCD (greatest common divisor) or the HCF (highest common factor).

I see you have correctly found GCF = 18. The squares are this to be 18 cm by 18 cm.

There will be $14 \times 9=126$ squares required.