Question

Select the GCF of these numbers. 48 and 60

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

Answer 1

The GCF of 48 and 60 is determined by comparing their prime factorizations and selecting the lowest powers of the common factors, which leads to 2² × 3. Hence, the correct option is a) 2² × 3.

Step-by-step explanation:

The Greatest Common Factor (GCF) of two numbers is the largest number that divides both of them without leaving a remainder. To find the GCF of 48 and 60, we should first express each number as the product of its prime factors:

• 48 = 24 × 31
• 60 = 22 × 31 × 51

Now, we compare the prime factorizations and take the lowest power of the common factors. In this case, that would be:

• 22 (since 24 and 22 are common, and the lowest power is 22)
• 31 (since 3 is common in both prime factorizations with the same power)

Therefore, the GCF is 22 × 31, which means the correct option is a) 22 × 3.