Answer:
Explanation:
Sure, I can help you with that! Let's go step by step:
**Express 75 as a product of prime numbers:**
To express 75 as a product of prime numbers, you can perform prime factorization:
75 = 3 * 25
Since 25 can be further broken down into 5 * 5:
75 = 3 * 5 * 5
So, the prime factorization of 75 is 3 * 5 * 5.
**Express 90 as a product of prime numbers:**
Similarly, let's express 90 as a product of prime numbers:
90 = 2 * 45
Further breaking down 45 into 3 * 15:
90 = 2 * 3 * 15
Breaking down 15 into 3 * 5:
90 = 2 * 3 * 3 * 5
So, the prime factorization of 90 is 2 * 3 * 3 * 5.
**Find the greatest common factor (GCF) of 75 and 90 using prime factors:**
To find the GCF of 75 and 90, you need to identify the common prime factors and multiply them together:
Common prime factors: 3 and 5
GCF = 3 * 5 = 15
**Determine the number of groups:**
The GCF of 75 and 90 is 15, and since the principal wants to divide the students into groups of equal size, the number of students in each group will be equal to the GCF, which is 15.
For the seventh graders (90 students):
Number of groups = Total number of students / Students per group
Number of groups = 90 / 15 = 6 groups
For the eighth graders (75 students):
Number of groups = Total number of students / Students per group
Number of groups = 75 / 15 = 5 groups
So, there will be a total of 6 + 5 = 11 groups formed for the trip to the zoo. Each group will consist of 15 students.