Highest Common Factor of 508, 686, 361 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 508, 686, 361 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 508, 686, 361 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 508, 686, 361 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 508, 686, 361 is 1.

HCF(508, 686, 361) = 1

HCF of 508, 686, 361 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 508, 686, 361 is 1.

Highest Common Factor of 508,686,361 using Euclid's algorithm

Highest Common Factor of 508,686,361 is 1

Step 1: Since 686 > 508, we apply the division lemma to 686 and 508, to get

686 = 508 x 1 + 178

Step 2: Since the reminder 508 ≠ 0, we apply division lemma to 178 and 508, to get

508 = 178 x 2 + 152

Step 3: We consider the new divisor 178 and the new remainder 152, and apply the division lemma to get

178 = 152 x 1 + 26

We consider the new divisor 152 and the new remainder 26,and apply the division lemma to get

152 = 26 x 5 + 22

We consider the new divisor 26 and the new remainder 22,and apply the division lemma to get

26 = 22 x 1 + 4

We consider the new divisor 22 and the new remainder 4,and apply the division lemma to get

22 = 4 x 5 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 508 and 686 is 2

Notice that 2 = HCF(4,2) = HCF(22,4) = HCF(26,22) = HCF(152,26) = HCF(178,152) = HCF(508,178) = HCF(686,508) .

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

Step 1: Since 361 > 2, we apply the division lemma to 361 and 2, to get

361 = 2 x 180 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 361 is 1

Notice that 1 = HCF(2,1) = HCF(361,2) .

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Frequently Asked Questions on HCF of 508, 686, 361 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 508, 686, 361?

Answer: HCF of 508, 686, 361 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 508, 686, 361 using Euclid's Algorithm?

Answer: For arbitrary numbers 508, 686, 361 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.