Euclidean Algorithm of 270 and 192

The GCF of 270 and 192 is 6.

Quick math

  • 270 = 1 × 192 + 78
  • 192 = 2 × 78 + 36
  • 78 = 2 × 36 + 6
  • 36 = 6 × 6 + 0
  • The last non-zero remainder is 6.
GCF
6
Division steps
4
LCM
8,640
Coprime
No
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Euclidean Algorithm for 270 and 192

The GCF of 270 and 192 is 6. The Euclidean algorithm finds it in 4 steps of division with remainder.

Handwritten notebook page running the Euclidean algorithm on 270 and 192
The Euclidean algorithm on 270 and 192 worked out by hand: the GCF is 6.

The Division Steps

  1. 270 = 1 × 192 + 78
  2. 192 = 2 × 78 + 36
  3. 78 = 2 × 36 + 6
  4. 36 = 6 × 6 + 0

Reading the Result

The last non-zero remainder is 6, so the GCF of 270 and 192 is 6. Both 270 and 192 divide evenly by 6.

The LCM of 270 and 192

LCM = 270 × 192 ÷ 6 = 8,640. Try other pairs in the Euclidean Algorithm Calculator.

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Euclidean Algorithm of 270 and 192: FAQs

What is the GCF of 270 and 192 by the Euclidean algorithm?

The GCF of 270 and 192 is 6. The steps are: 270 = 1 × 192 + 78; 192 = 2 × 78 + 36; 78 = 2 × 36 + 6; 36 = 6 × 6 + 0. The last non-zero remainder is 6.

How does the Euclidean algorithm work?

Divide the larger number by the smaller one and keep the remainder. Then divide the smaller number by that remainder, and repeat until the remainder is 0. The last non-zero remainder is the GCF.

How many steps does it take for 270 and 192?

It takes 4 division steps to reach a remainder of 0.

What is the LCM of 270 and 192?

The LCM of 270 and 192 is 8,640, found by dividing 270 × 192 by the GCF 6.

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