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Greatest Common Divisor (GCD) of 167 and 104

The greatest common divisor (GCD) of 167 and 104 is 1.

What is the Greatest Common Divisor (GCD)?

The GCD of two integers is the largest positive integer that divides both numbers without leaving a remainder. It is useful in simplifying fractions, finding common factors, and in number theory.

How to Calculate the GCD of 167 and 104?

We use the Euclidean algorithm, which involves the following steps:

  1. Divide the larger number by the smaller number.
  2. Replace the larger number with the smaller number and the smaller number with the remainder from the division.
  3. Repeat this process until the remainder is zero.
  4. The non-zero remainder just before zero is the GCD.

Step-by-Step Euclidean Algorithm

StepCalculation
1 167 ÷ 104 = 1 remainder 63
2 104 ÷ 63 = 1 remainder 41
3 63 ÷ 41 = 1 remainder 22
4 41 ÷ 22 = 1 remainder 19
5 22 ÷ 19 = 1 remainder 3
6 19 ÷ 3 = 6 remainder 1
7 3 ÷ 1 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
120 and 7515
75 and 1061
46 and 1342
198 and 1451
157 and 681

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