Highest Common Factor of 831, 531, 421 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, 531, 421 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 831, 531, 421 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, 531, 421 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, 531, 421 is 1.

HCF(831, 531, 421) = 1

HCF of 831, 531, 421 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, 531, 421 is 1.

Highest Common Factor of 831,531,421 using Euclid's algorithm

Highest Common Factor of 831,531,421 is 1

Step 1: Since 831 > 531, we apply the division lemma to 831 and 531, to get

831 = 531 x 1 + 300

Step 2: Since the reminder 531 ≠ 0, we apply division lemma to 300 and 531, to get

531 = 300 x 1 + 231

Step 3: We consider the new divisor 300 and the new remainder 231, and apply the division lemma to get

300 = 231 x 1 + 69

We consider the new divisor 231 and the new remainder 69,and apply the division lemma to get

231 = 69 x 3 + 24

We consider the new divisor 69 and the new remainder 24,and apply the division lemma to get

69 = 24 x 2 + 21

We consider the new divisor 24 and the new remainder 21,and apply the division lemma to get

24 = 21 x 1 + 3

We consider the new divisor 21 and the new remainder 3,and apply the division lemma to get

21 = 3 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 831 and 531 is 3

Notice that 3 = HCF(21,3) = HCF(24,21) = HCF(69,24) = HCF(231,69) = HCF(300,231) = HCF(531,300) = HCF(831,531) .

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

Step 1: Since 421 > 3, we apply the division lemma to 421 and 3, to get

421 = 3 x 140 + 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 421 is 1

Notice that 1 = HCF(3,1) = HCF(421,3) .

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, 531, 421 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, 531, 421?

Answer: HCF of 831, 531, 421 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 831, 531, 421 using Euclid's Algorithm?

Answer: For arbitrary numbers 831, 531, 421 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.