Highest Common Factor of 840, 861 using Euclid's algorithm

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 840, 861 i.e. 21 the largest integer that leaves a remainder zero for all numbers.

HCF of 840, 861 is 21 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.

Consider we have numbers 840, 861 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b

Highest common factor (HCF) of 840, 861 is 21.

HCF(840, 861) = 21

HCF of 840, 861 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

HCF of:

Highest common factor (HCF) of 840, 861 is 21.

Highest Common Factor of 840,861 using Euclid's algorithm

Highest Common Factor of 840,861 is 21

Step 1: Since 861 > 840, we apply the division lemma to 861 and 840, to get

861 = 840 x 1 + 21

Step 2: Since the reminder 840 ≠ 0, we apply division lemma to 21 and 840, to get

840 = 21 x 40 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 840 and 861 is 21

Notice that 21 = HCF(840,21) = HCF(861,840) .

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Frequently Asked Questions on HCF of 840, 861 using Euclid's Algorithm

1. What is the Euclid division algorithm?

Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.

2. what is the HCF of 840, 861?

Answer: HCF of 840, 861 is 21 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 840, 861 using Euclid's Algorithm?

Answer: For arbitrary numbers 840, 861 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.