Highest Common Factor of 831, 216, 862 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 831, 216, 862 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 831, 216, 862 is 1 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 831, 216, 862 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 831, 216, 862 is 1.

HCF(831, 216, 862) = 1

HCF of 831, 216, 862 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 831, 216, 862 is 1.

Highest Common Factor of 831,216,862 using Euclid's algorithm

Highest Common Factor of 831,216,862 is 1

Step 1: Since 831 > 216, we apply the division lemma to 831 and 216, to get

831 = 216 x 3 + 183

Step 2: Since the reminder 216 ≠ 0, we apply division lemma to 183 and 216, to get

216 = 183 x 1 + 33

Step 3: We consider the new divisor 183 and the new remainder 33, and apply the division lemma to get

183 = 33 x 5 + 18

We consider the new divisor 33 and the new remainder 18,and apply the division lemma to get

33 = 18 x 1 + 15

We consider the new divisor 18 and the new remainder 15,and apply the division lemma to get

18 = 15 x 1 + 3

We consider the new divisor 15 and the new remainder 3,and apply the division lemma to get

15 = 3 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 831 and 216 is 3

Notice that 3 = HCF(15,3) = HCF(18,15) = HCF(33,18) = HCF(183,33) = HCF(216,183) = HCF(831,216) .

We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma

Step 1: Since 862 > 3, we apply the division lemma to 862 and 3, to get

862 = 3 x 287 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 862 is 1

Notice that 1 = HCF(3,1) = HCF(862,3) .

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Frequently Asked Questions on HCF of 831, 216, 862 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 831, 216, 862?

Answer: HCF of 831, 216, 862 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 831, 216, 862 using Euclid's Algorithm?

Answer: For arbitrary numbers 831, 216, 862 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.