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Greatest Common Divisor (GCD) of 158 and 102

The greatest common divisor (GCD) of 158 and 102 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 158 and 102?

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
1 158 ÷ 102 = 1 remainder 56
2 102 ÷ 56 = 1 remainder 46
3 56 ÷ 46 = 1 remainder 10
4 46 ÷ 10 = 4 remainder 6
5 10 ÷ 6 = 1 remainder 4
6 6 ÷ 4 = 1 remainder 2
7 4 ÷ 2 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
164 and 1911
42 and 126
53 and 1091
74 and 1242
152 and 1011

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