Euclidean Algorithm of 252 and 105

The GCF of 252 and 105 is 21.

Quick math

  • 252 = 2 × 105 + 42
  • 105 = 2 × 42 + 21
  • 42 = 2 × 21 + 0
  • The last non-zero remainder is 21.
GCF
21
Division steps
3
LCM
1,260
Coprime
No
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Euclidean Algorithm for 252 and 105

The GCF of 252 and 105 is 21. The Euclidean algorithm finds it in 3 steps of division with remainder.

Handwritten notebook page running the Euclidean algorithm on 252 and 105
The Euclidean algorithm on 252 and 105 worked out by hand: the GCF is 21.

The Division Steps

  1. 252 = 2 × 105 + 42
  2. 105 = 2 × 42 + 21
  3. 42 = 2 × 21 + 0

Reading the Result

The last non-zero remainder is 21, so the GCF of 252 and 105 is 21. Both 252 and 105 divide evenly by 21.

The LCM of 252 and 105

LCM = 252 × 105 ÷ 21 = 1,260. Try other pairs in the Euclidean Algorithm Calculator.

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Euclidean Algorithm of 252 and 105: FAQs

What is the GCF of 252 and 105 by the Euclidean algorithm?

The GCF of 252 and 105 is 21. The steps are: 252 = 2 × 105 + 42; 105 = 2 × 42 + 21; 42 = 2 × 21 + 0. The last non-zero remainder is 21.

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 252 and 105?

It takes 3 division steps to reach a remainder of 0.

What is the LCM of 252 and 105?

The LCM of 252 and 105 is 1,260, found by dividing 252 × 105 by the GCF 21.

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