Question 2 options:
Find the GCF of these numbers.
120, 72
The GCF (Greatest Common Factor) of 120 and 72 is 24.
To find the Greatest Common Factor (GCF) of 120 and 72, follow these steps:
Step 1: List the factors of each number.
The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.
Step 2: Identify the common factors.
The common factors are 1, 2, 3, 4, 6, 8, 12, and 24.
Step 3: Determine the greatest common factor.
The GCF is the largest common factor, which is 24.
Therefore, the GCF of 120 and 72 is 24.
To find the greatest common factor (GCF) of two numbers, such as 120 and 72, follow these steps:
1. Prime Factorization: Express each number as a product of prime factors.
- Prime factorization of 120: 2^3 * 3 * 5
- Prime factorization of 72: 2^3 * 3^2
2. Identify Common Prime Factors: Look for the prime factors that both numbers share.
- In this case, both numbers have 2^3 and 3 in common.
3. Find the Smallest Exponent: Compare the exponents of the common prime factors and choose the smallest exponent.
- The common prime factor 2^3 has exponent 3 in both numbers.
- The common prime factor 3 has exponent 1 in one number and exponent 2 in the other number.
- Choosing the smallest exponent for each common prime factor, we have 2^3 * 3^1, which is equal to 24.
Therefore, the greatest common factor (GCF) of 120 and 72 is 24.