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)
To find the greatest number of gift boxes that can be put together with the given number of bars, we need to find the greatest common divisor (GCD) of 75 and 45.
The prime factorization of 75 is 5 × 5 × 3, and the prime factorization of 45 is 5 × 3 × 3.
To find the GCD, we take the highest power of each common prime factor:
- The highest power of 5 is 5 × 3 = 15.
- The highest power of 3 is 3 × 3 = 9.
Therefore, the GCD of 75 and 45 is 15.
Since each gift box will contain exactly the same bars, we can make 15 gift boxes with 75 mint chocolate bars and 45 caramel pecan bars.
Answer: The greatest number of gift boxes that can be put together is 15.