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Greatest Common Divisor (GCD) of 90 and 147

The greatest common divisor (GCD) of 90 and 147 is 3.

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 90 and 147?

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 90 ÷ 147 = 0 remainder 90
2 147 ÷ 90 = 1 remainder 57
3 90 ÷ 57 = 1 remainder 33
4 57 ÷ 33 = 1 remainder 24
5 33 ÷ 24 = 1 remainder 9
6 24 ÷ 9 = 2 remainder 6
7 9 ÷ 6 = 1 remainder 3
8 6 ÷ 3 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
56 and 331
109 and 1541
200 and 1062
126 and 262
138 and 311

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