What is the greatest common factor for 45 and 180?

The greatest common factor (GCF) for 45 and 180 is 45.

To find the GCF, we start by determining the prime factorization of both numbers. For 45, the prime factorization is:

• 45 = 3 × 3 × 5 (or 3² × 5)

For 180, the prime factorization is:

• 180 = 2 × 2 × 3 × 3 × 5 (or 2² × 3² × 5)

Next, we identify the common prime factors in both numbers:

• Both 45 and 180 have the prime factors 3 and 5.

Now, we take the lowest power of each of these common factors:

• For the prime factor 3, the lowest power is 3² from 45.
• For the prime factor 5, the lowest power is 5¹ from both numbers.

Now, we multiply these together to find the GCF:

• GCF = 3² × 5¹ = 9 × 5 = 45.

Thus, the greatest common factor of 45 and 180 is 45.