Question

Select the GCF of these numbers. 48 and 60

a. 3²
b. 2³· 5
c. 13· 19³· 23²
d. 2· 11²
e. 2²· 3

Answer 1

The Greatest Common Factor (GCF) of the numbers 48 and 60 is 2² × 3, which equals 12. The correct answer from the provided options is e. 2² × 3.

Step-by-step explanation:

The student has asked to select the Greatest Common Factor (GCF) of the numbers 48 and 60. To find the GCF, we will first factor both numbers into their prime factors:

• 48 = 2´ × 3¹ (2 × 2 × 2 × 2 × 3)
• 60 = 2² × 3¹ × 5¹ (2 × 2 × 3 × 5)

We find the common prime factors and choose the lowest powers of these factors from both numbers:

• The common prime factors are 2 and 3.
• The lowest powers for these primes are 2² and 3¹.

Therefore, the GCF of 48 and 60 is 2² × 3 = 4 × 3 = 12.

Looking at the options, the correct answer is:

e. 2² × 3