The yearbook editor wants each page of the Activities section of the yearbook to have the same combination of colour photos and black-and-white photos. If there are 38 colour photos and 19 black-and-white photos, all of which the editor wants to use, what is the greatest number of Activities pages the editor can create?
Question
The yearbook editor wants each page of the Activities section of the yearbook to have the same combination of colour photos and black-and-white photos. If there are 38 colour photos and 19 black-and-white photos, all of which the editor wants to use, what is the greatest number of Activities pages the editor can create?
Solution
To solve this problem, we need to find the greatest common divisor (GCD) of the number of colour photos and the number of black-and-white photos. The GCD is the largest number that can divide both numbers without leaving a remainder.
Here are the steps:
- List the divisors of 38: 1, 2, 19, 38
- List the divisors of 19: 1, 19
- Identify the greatest number that appears in both lists: 19
So, the greatest number of Activities pages the editor can create, where each page has the same combination of colour photos and black-and-white photos, is 19.
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