What is GCD(75, 4)?

The GCD (Greatest Common Divisor) is the largest number that can divide two (or more) numbers without leaving a remainder.

The GCD of 75 and 4 is 1.

How to compute GCD(75, 4)

Comparing the divisors of 75 and 4

This first method consists in listing the divisors of the two numbers and then identifying the largest one they have in common.

Divisors of 75:

1, 3, 5, 15, 25, 75

Divisors of 4:

1, 2, 4

We can see from these two lists that the greatest divisor they have in common is: 1

For small numbers, this can be done quickly. However, as numbers increase, the list of potential divisors grows longer, making this method cumbersome and less practical.

Euclid's algorithm

Fortunately, there's a much more efficient method: Euclid's algorithm. It's particularly well-suited to larger numbers. Here's how it works:

  1. Divide 75 by 4. The quotient is 18 and the remainder is 3.
  2. The previous divisor (4) is now the dividend. The remainder (3) is the new divisor. Divide 4 by 3. The quotient is 1 and the remainder is 1.
  3. The previous divisor (3) is now the dividend. The remainder (1) is the new divisor. Divide 3 by 1. The quotient is 3 and the remainder is 0.
  4. When you reach a remainder of 0, the last divisor (in this case, 1) is the GCD.