Question

A field trip is being planned for the 9th and 10th graders of AHS. There will be 80 ninth graders and 65 tenth graders. The trip coordinator wants groups with an equal number of students from each grade. Use prime factorization to find the Greatest common factor to determine the size of the groups.

A. The greatest common factor is 5.
B. The greatest common factor is 15.
C. The greatest common factor is 10.
D. The greatest common factor is 20.

Answer 1

To find the size of the groups, we need to find the greatest common factor (GCF) of the number of ninth graders (80) and tenth graders (65). The prime factorization of 80 and 65 can help us determine the GCF, which is 20. Hence, D) is correct.

Step-by-step explanation:

To find the size of the groups, we need to find the greatest common factor (GCF) of the number of ninth graders (80) and tenth graders (65). Prime factorization can help us determine the GCF.

Start by finding the prime factors of 80 and 65:

1. 80 = 2 * 2 * 2 * 2 * 5
2. 65 = 5 * 13

Now, we look for common prime factors in the two numbers: 2 * 2 * 2 * 2 * 5. The GCF is the product of these common factors, which is 2 * 2 * 5 = 20.

Therefore, the correct answer is D. The greatest common factor is 20.