Highest Common Factor of 566, 898, 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 566, 898, 231 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 566, 898, 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 566, 898, 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 566, 898, 231 is 1.

HCF(566, 898, 231) = 1

HCF of 566, 898, 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 566, 898, 231 is 1.

Highest Common Factor of 566,898,231 using Euclid's algorithm

Highest Common Factor of 566,898,231 is 1

Step 1: Since 898 > 566, we apply the division lemma to 898 and 566, to get

898 = 566 x 1 + 332

Step 2: Since the reminder 566 ≠ 0, we apply division lemma to 332 and 566, to get

566 = 332 x 1 + 234

Step 3: We consider the new divisor 332 and the new remainder 234, and apply the division lemma to get

332 = 234 x 1 + 98

We consider the new divisor 234 and the new remainder 98,and apply the division lemma to get

234 = 98 x 2 + 38

We consider the new divisor 98 and the new remainder 38,and apply the division lemma to get

98 = 38 x 2 + 22

We consider the new divisor 38 and the new remainder 22,and apply the division lemma to get

38 = 22 x 1 + 16

We consider the new divisor 22 and the new remainder 16,and apply the division lemma to get

22 = 16 x 1 + 6

We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get

16 = 6 x 2 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 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 566 and 898 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(22,16) = HCF(38,22) = HCF(98,38) = HCF(234,98) = HCF(332,234) = HCF(566,332) = HCF(898,566) .

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 566, 898, 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 566, 898, 231?

Answer: HCF of 566, 898, 231 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 566, 898, 231 using Euclid's Algorithm?

Answer: For arbitrary numbers 566, 898, 231 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.