Question

A florist has 30 carnations and 42 roses. He wants to put the flowers in vases so that each vase has the same number of flowers

Answer 1

Note that

• 30=2·3·5;
• 42=2·3·7.

Find the grearest common factor GCF(30,42). You can see that numbers 30 and 42 have common factors 2 and 3, then

$GCF(30,42)=2\cdot 3=6.$

This gives that the greatest number of identical vases florist can fill is 6. Each vase will contain

• $30:6=5$ carnations;
• $42:6=7$ roses.

Therefore, in each vase will be 12 flowers (5 carnations and 7 roses).