You are making 75 mint chocolate bars and 45 caramel pecan bars for some gift boxes. If each box will contain exactly the same bars, what is the greatest number of gift boxes you can put together?(1 point)
Responses
5
5
15
15
25
25
45
45
The greatest number of gift boxes that can be put together is 15.
To find this, we need to determine the highest common factor of 75 and 45.
The prime factorization of 75 is 3 * 5 * 5 and the prime factorization of 45 is 3 * 3 * 5.
To find the highest common factor, we take the highest power of each prime factor that appears in both factorizations. In this case, the highest power of 3 is 3^1 and the highest power of 5 is 5^1.
Therefore, the highest common factor is 3^1 * 5^1 = 15.
So, you can put together 15 gift boxes with exactly the same bars.