Step 1a

To find the largest common factor (also known as the greatest common divisor or GCD) of two numbers, in this case, 75 and 125, you can use the prime factorization method.

Step 1: Prime factorization of 75:

\$ 75 = 3^1 * 5^2 \$

Step 2: Prime factorization of 125:

\$125 = 5^3 \$.

Explanation: Here, we used the prime factorization method for both numbers.

Step 1b

Step 3: Identify the common prime factors and their lowest powers:

The common prime factor is 5.

The lowest power of 5 is \$5^1\$.

Explanation: Here, we discuss a common prime factor is 5 and the lowest power of 5 is \$5^1\$.

Step 1c

Step 4: Multiply the common prime factors with their lowest powers together:

GCD(75, 125) = 5^1 = 5

So, the largest common factor of 75 and 125 is 5.

Explanation: Here, we multiply the common prime factor of both numbers is 5.