Ronald is distributing writing supplies to campers. He must give the same number of supplies to each camper and use all the supplies. He has 14 pencils and 21 note pads. What is the greatest number of campers he can give writing supplies?

Robert can give writing supplies to at most 7 campers.

Step-by-step explanation:

The problem states that Robert must give the same number of supplies to each camper and use all the supplies. It means that the greatest number of campers that Robert can give writing supplies is the greatest common divisor (gcd) between the number of pencils and the number of note pads.

The gcd between two integers is the largest positive number that divides each of the integers. We can find this value by prime factorization.

The problem states that he has 14 pencils and 21 note pads. So we have to find gcd (14,21).

21 is not divisible by 2, so we try factoring by 3

14 is not divisible by 3, so we try factoring by 5

None of them are divisible by 5, so we move to 7

Both are divisible by 7, so

14 - 21 | 7

2 - 3

2<7, 3<7, so gcd (14,21) = 7.

Robert can give writing supplies to at most 7 campers.