Highest Common Factor of 252, 682, 231 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 252, 682, 231 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 252, 682, 231 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 252, 682, 231 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 252, 682, 231 is 1.

HCF(252, 682, 231) = 1

HCF of 252, 682, 231 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 252, 682, 231 is 1.

Highest Common Factor of 252,682,231 using Euclid's algorithm

Highest Common Factor of 252,682,231 is 1

Step 1: Since 682 > 252, we apply the division lemma to 682 and 252, to get

682 = 252 x 2 + 178

Step 2: Since the reminder 252 ≠ 0, we apply division lemma to 178 and 252, to get

252 = 178 x 1 + 74

Step 3: We consider the new divisor 178 and the new remainder 74, and apply the division lemma to get

178 = 74 x 2 + 30

We consider the new divisor 74 and the new remainder 30,and apply the division lemma to get

74 = 30 x 2 + 14

We consider the new divisor 30 and the new remainder 14,and apply the division lemma to get

30 = 14 x 2 + 2

We consider the new divisor 14 and the new remainder 2,and apply the division lemma to get

14 = 2 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 252 and 682 is 2

Notice that 2 = HCF(14,2) = HCF(30,14) = HCF(74,30) = HCF(178,74) = HCF(252,178) = HCF(682,252) .

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

Step 1: Since 231 > 2, we apply the division lemma to 231 and 2, to get

231 = 2 x 115 + 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 231 is 1

Notice that 1 = HCF(2,1) = HCF(231,2) .

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Frequently Asked Questions on HCF of 252, 682, 231 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 252, 682, 231?

Answer: HCF of 252, 682, 231 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 252, 682, 231 using Euclid's Algorithm?

Answer: For arbitrary numbers 252, 682, 231 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.