Highest Common Factor of 231, 598, 108 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 231, 598, 108 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 231, 598, 108 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 231, 598, 108 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 231, 598, 108 is 1.

HCF(231, 598, 108) = 1

HCF of 231, 598, 108 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 231, 598, 108 is 1.

Highest Common Factor of 231,598,108 using Euclid's algorithm

Highest Common Factor of 231,598,108 is 1

Step 1: Since 598 > 231, we apply the division lemma to 598 and 231, to get

598 = 231 x 2 + 136

Step 2: Since the reminder 231 ≠ 0, we apply division lemma to 136 and 231, to get

231 = 136 x 1 + 95

Step 3: We consider the new divisor 136 and the new remainder 95, and apply the division lemma to get

136 = 95 x 1 + 41

We consider the new divisor 95 and the new remainder 41,and apply the division lemma to get

95 = 41 x 2 + 13

We consider the new divisor 41 and the new remainder 13,and apply the division lemma to get

41 = 13 x 3 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 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 231 and 598 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(41,13) = HCF(95,41) = HCF(136,95) = HCF(231,136) = HCF(598,231) .

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

Step 1: Since 108 > 1, we apply the division lemma to 108 and 1, to get

108 = 1 x 108 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 108 is 1

Notice that 1 = HCF(108,1) .

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Frequently Asked Questions on HCF of 231, 598, 108 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 231, 598, 108?

Answer: HCF of 231, 598, 108 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 231, 598, 108 using Euclid's Algorithm?

Answer: For arbitrary numbers 231, 598, 108 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.