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Greatest Common Divisor (GCD) of 156 and 179

The greatest common divisor (GCD) of 156 and 179 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 156 and 179?

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
1 156 ÷ 179 = 0 remainder 156
2 179 ÷ 156 = 1 remainder 23
3 156 ÷ 23 = 6 remainder 18
4 23 ÷ 18 = 1 remainder 5
5 18 ÷ 5 = 3 remainder 3
6 5 ÷ 3 = 1 remainder 2
7 3 ÷ 2 = 1 remainder 1
8 2 ÷ 1 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
40 and 691
98 and 1202
179 and 1781
172 and 1971
150 and 555

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