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Greatest Common Divisor (GCD) of 34 and 48

The greatest common divisor (GCD) of 34 and 48 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 34 and 48?

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 34 ÷ 48 = 0 remainder 34
2 48 ÷ 34 = 1 remainder 14
3 34 ÷ 14 = 2 remainder 6
4 14 ÷ 6 = 2 remainder 2
5 6 ÷ 2 = 3 remainder 0

Examples of GCD Calculations

NumbersGCD
199 and 191
70 and 1782
49 and 661
59 and 1311
112 and 571

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