What is the greatest common factor (GCF) of 20 and 30?

To determine the greatest common factor (GCF) of 20 and 30, we start by identifying the prime factorization of each number.

The number 20 can be factored into primes as follows:

• 20 = 2 × 2 × 5 or 2² × 5.

The number 30 can be factored into primes as:

• 30 = 2 × 3 × 5.

Next, we look for the common factors from these factorizations. Both numbers share the prime factors 2 and 5.

Now, we take the lowest power of each common prime:

• For 2, the lowest power is 2¹.

• For 5, the lowest power is 5¹.

Now, multiply these together to find the GCF:

• GCF = 2¹ × 5¹ = 2 × 5 = 10.

Thus, the greatest common factor of 20 and 30 is indeed 10. This demonstrates that the correct answer is the value representing the largest factor that both original numbers share, which in this case is 10.