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Greatest Common Divisor (GCD) of 113 and 169

The greatest common divisor (GCD) of 113 and 169 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 113 and 169?

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
1 113 ÷ 169 = 0 remainder 113
2 169 ÷ 113 = 1 remainder 56
3 113 ÷ 56 = 2 remainder 1
4 56 ÷ 1 = 56 remainder 0

Examples of GCD Calculations

NumbersGCD
170 and 1211
112 and 16856
11 and 261
124 and 1342
84 and 1091

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