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Greatest Common Divisor (GCD) of 80 and 45

The greatest common divisor (GCD) of 80 and 45 is 5.

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 80 and 45?

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 80 ÷ 45 = 1 remainder 35
2 45 ÷ 35 = 1 remainder 10
3 35 ÷ 10 = 3 remainder 5
4 10 ÷ 5 = 2 remainder 0

Examples of GCD Calculations

NumbersGCD
22 and 1622
154 and 19614
49 and 1671
99 and 4411
87 and 1281

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