2. you are making necklaces for your friends. you have 72 blue beads and 42 red beads. each friend will receive an identical necklace, and all beads must be used

To find out the number of necklaces that can be made from 72 and 42 beads, think of the Greatest Common Factor of both numbers

Factors of 72
1 × 72
2 × 36 
3 × 24
4 × 18
6 × 12
8 × 9

Factors of 42
1 × 42
2 × 21 
3 × 14
6 × 7

The Greatest Common Factor is 6, so there are 6 necklaces can be made with equal number of beads