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

A. what is the Greatest number of identical vases he can fill?

B. How many flowers will be in each vase?

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).