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Greatest Common Divisor (GCD) of 88 and 62

The greatest common divisor (GCD) of 88 and 62 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 88 and 62?

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 88 ÷ 62 = 1 remainder 26
2 62 ÷ 26 = 2 remainder 10
3 26 ÷ 10 = 2 remainder 6
4 10 ÷ 6 = 1 remainder 4
5 6 ÷ 4 = 1 remainder 2
6 4 ÷ 2 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
22 and 11022
27 and 1461
136 and 1051
80 and 662
153 and 1413

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