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Greatest Common Divisor (GCD) of 62 and 140

The greatest common divisor (GCD) of 62 and 140 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 140?

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 ÷ 140 = 0 remainder 62
2 140 ÷ 62 = 2 remainder 16
3 62 ÷ 16 = 3 remainder 14
4 16 ÷ 14 = 1 remainder 2
5 14 ÷ 2 = 7 remainder 0

Examples of GCD Calculations

NumbersGCD
123 and 1173
188 and 1844
168 and 573
16 and 1782
113 and 1051

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