Euclidean Algorithm of 1,071 and 462

The GCF of 1,071 and 462 is 21.

Quick math

  • 1,071 = 2 × 462 + 147
  • 462 = 3 × 147 + 21
  • 147 = 7 × 21 + 0
  • The last non-zero remainder is 21.
GCF
21
Division steps
3
LCM
23,562
Coprime
No
Try your own numbers

Euclidean Algorithm for 1,071 and 462

The GCF of 1,071 and 462 is 21. The Euclidean algorithm finds it in 3 steps of division with remainder.

Handwritten notebook page running the Euclidean algorithm on 1,071 and 462
The Euclidean algorithm on 1,071 and 462 worked out by hand: the GCF is 21.

The Division Steps

  1. 1,071 = 2 × 462 + 147
  2. 462 = 3 × 147 + 21
  3. 147 = 7 × 21 + 0

Reading the Result

The last non-zero remainder is 21, so the GCF of 1,071 and 462 is 21. Both 1,071 and 462 divide evenly by 21.

The LCM of 1,071 and 462

LCM = 1,071 × 462 ÷ 21 = 23,562. Try other pairs in the Euclidean Algorithm Calculator.

More Euclidean Algorithm Calculator Examples

Euclidean Algorithm of 1,071 and 462: FAQs

What is the GCF of 1,071 and 462 by the Euclidean algorithm?

The GCF of 1,071 and 462 is 21. The steps are: 1,071 = 2 × 462 + 147; 462 = 3 × 147 + 21; 147 = 7 × 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 1,071 and 462?

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

What is the LCM of 1,071 and 462?

The LCM of 1,071 and 462 is 23,562, found by dividing 1,071 × 462 by the GCF 21.

More Worked Examples

Showing 3 of 3 examples