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Greatest Common Divisor (GCD) of 62 and 52

The greatest common divisor (GCD) of 62 and 52 is 2.

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 62 and 52?

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 62 ÷ 52 = 1 remainder 10
2 52 ÷ 10 = 5 remainder 2
3 10 ÷ 2 = 5 remainder 0

Examples of GCD Calculations

NumbersGCD
169 and 1051
55 and 1261
70 and 1742
161 and 711
200 and 391

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