100pts: Explain the how to use the Euclidean algorithm for finding the GCF of 675 and 150

Greatest (highest) common factor (divisor)

gcf, hcf, gcd (675; 150) = 75 = 3 * 52;

The numbers have common prime factors.

Step-by-step explanation:

675 = 33 * 52;

150 = 2 * 3 * 52;

Multiply all the common prime factors, by the lowest exponents.

Greatest (highest) common factor (divisor):

gcf, hcf, gcd (675; 150) = 3 * 52

Step 1. Divide the larger number by the smaller one:

675 : 150 = 4 + 75;

Step 2. Divide the smaller number by the above operation's remainder:

150 : 75 = 2 + 0;

At this step, the remainder is zero, so we stop:

75 is the number we were looking for, the last remainder that is not zero.

This is the greatest common factor (divisor).

Greatest (highest) common factor (divisor):

gcf, hcf, gcd (675; 150) = 75

gcf, hcf, gcd (675; 150) = 75 = 3 * 52