Question

1. model with mathematics write and solve a real - world problem that can be solved using the greatest common factor of two numbers.

Explanation:

Step1: Define real-world scenario

A teacher has 24 pencils and 36 erasers. She wants to make identical supply kits for students, using all supplies. What is the maximum number of kits she can make, and how many pencils/erasers are in each kit?

Step2: Identify GCF target

We need GCF of 24 and 36. Prime factorize both numbers:
$24 = 2^3 \times 3^1$
$36 = 2^2 \times 3^2$

Step3: Calculate GCF

Multiply lowest power of shared primes:
$\text{GCF}(24,36) = 2^2 \times 3^1 = 4 \times 3 = 12$

Step4: Find per-kit quantities

Pencils per kit: $\frac{24}{12} = 2$
Erasers per kit: $\frac{36}{12} = 3$

Answer:

Real-world problem: A teacher has 24 pencils and 36 erasers. She wants to create identical supply kits for her students, using up all the pencils and erasers. What is the maximum number of kits she can make, and how many pencils and erasers will be in each kit?
Solution: The maximum number of kits is 12. Each kit will contain 2 pencils and 3 erasers.