Question

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. What is the greatest number of friends who can receive a necklace?

Answer 1

6 friends

Explanation:

In a question like this, you are trying to find the Highest Common Denominator, or HCF. This can be done manually, by finding all the factors of 42 `(1,2,3,6,7,14,21,42)`, all the factors of 72 `(1,2,3,4,6,8,9,12,18,24,36,72)`, and comparing them to see that their HCF is `6`. Or, it can be done by dividing both numbers,
`=72/42`, simplifying the fraction

`=12/7`, then dividing the starting number with the new simplifiied number, remembering always to divide numerator with numerator and denominator with denominator.
`72/12=6` or `42/7=6`

This process works with any two numbers which you want to find the HCF of, and can be simplified into this rule:
If `a=` any number, `b=` any number and `c/d` is the simplified fraction of `a/b`,

The HCF `=a/c` or `=b/d`

I hope that helped!