Highest Common Factor of 831, 643, 36 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, 643, 36 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 831, 643, 36 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, 643, 36 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, 643, 36 is 1.

HCF(831, 643, 36) = 1

HCF of 831, 643, 36 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, 643, 36 is 1.

Highest Common Factor of 831,643,36 using Euclid's algorithm

Highest Common Factor of 831,643,36 is 1

Step 1: Since 831 > 643, we apply the division lemma to 831 and 643, to get

831 = 643 x 1 + 188

Step 2: Since the reminder 643 ≠ 0, we apply division lemma to 188 and 643, to get

643 = 188 x 3 + 79

Step 3: We consider the new divisor 188 and the new remainder 79, and apply the division lemma to get

188 = 79 x 2 + 30

We consider the new divisor 79 and the new remainder 30,and apply the division lemma to get

79 = 30 x 2 + 19

We consider the new divisor 30 and the new remainder 19,and apply the division lemma to get

30 = 19 x 1 + 11

We consider the new divisor 19 and the new remainder 11,and apply the division lemma to get

19 = 11 x 1 + 8

We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get

11 = 8 x 1 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 831 and 643 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(19,11) = HCF(30,19) = HCF(79,30) = HCF(188,79) = HCF(643,188) = HCF(831,643) .

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

Step 1: Since 36 > 1, we apply the division lemma to 36 and 1, to get

36 = 1 x 36 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 36 is 1

Notice that 1 = HCF(36,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 831, 643, 36 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, 643, 36?

Answer: HCF of 831, 643, 36 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 831, 643, 36 using Euclid's Algorithm?

Answer: For arbitrary numbers 831, 643, 36 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.