Highest Common Factor of 691, 502, 461 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 691, 502, 461 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 691, 502, 461 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 691, 502, 461 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 691, 502, 461 is 1.

HCF(691, 502, 461) = 1

HCF of 691, 502, 461 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 691, 502, 461 is 1.

Highest Common Factor of 691,502,461 using Euclid's algorithm

Highest Common Factor of 691,502,461 is 1

Step 1: Since 691 > 502, we apply the division lemma to 691 and 502, to get

691 = 502 x 1 + 189

Step 2: Since the reminder 502 ≠ 0, we apply division lemma to 189 and 502, to get

502 = 189 x 2 + 124

Step 3: We consider the new divisor 189 and the new remainder 124, and apply the division lemma to get

189 = 124 x 1 + 65

We consider the new divisor 124 and the new remainder 65,and apply the division lemma to get

124 = 65 x 1 + 59

We consider the new divisor 65 and the new remainder 59,and apply the division lemma to get

65 = 59 x 1 + 6

We consider the new divisor 59 and the new remainder 6,and apply the division lemma to get

59 = 6 x 9 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 691 and 502 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(59,6) = HCF(65,59) = HCF(124,65) = HCF(189,124) = HCF(502,189) = HCF(691,502) .

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

Step 1: Since 461 > 1, we apply the division lemma to 461 and 1, to get

461 = 1 x 461 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 461 is 1

Notice that 1 = HCF(461,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 691, 502, 461 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 691, 502, 461?

Answer: HCF of 691, 502, 461 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 691, 502, 461 using Euclid's Algorithm?

Answer: For arbitrary numbers 691, 502, 461 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.