Highest Common Factor of 566, 877, 34 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, 877, 34 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 566, 877, 34 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, 877, 34 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, 877, 34 is 1.

HCF(566, 877, 34) = 1

HCF of 566, 877, 34 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, 877, 34 is 1.

Highest Common Factor of 566,877,34 using Euclid's algorithm

Highest Common Factor of 566,877,34 is 1

Step 1: Since 877 > 566, we apply the division lemma to 877 and 566, to get

877 = 566 x 1 + 311

Step 2: Since the reminder 566 ≠ 0, we apply division lemma to 311 and 566, to get

566 = 311 x 1 + 255

Step 3: We consider the new divisor 311 and the new remainder 255, and apply the division lemma to get

311 = 255 x 1 + 56

We consider the new divisor 255 and the new remainder 56,and apply the division lemma to get

255 = 56 x 4 + 31

We consider the new divisor 56 and the new remainder 31,and apply the division lemma to get

56 = 31 x 1 + 25

We consider the new divisor 31 and the new remainder 25,and apply the division lemma to get

31 = 25 x 1 + 6

We consider the new divisor 25 and the new remainder 6,and apply the division lemma to get

25 = 6 x 4 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 566 and 877 is 1

Notice that 1 = HCF(6,1) = HCF(25,6) = HCF(31,25) = HCF(56,31) = HCF(255,56) = HCF(311,255) = HCF(566,311) = HCF(877,566) .

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

Step 1: Since 34 > 1, we apply the division lemma to 34 and 1, to get

34 = 1 x 34 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 34 is 1

Notice that 1 = HCF(34,1) .

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Frequently Asked Questions on HCF of 566, 877, 34 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, 877, 34?

Answer: HCF of 566, 877, 34 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 566, 877, 34 using Euclid's Algorithm?

Answer: For arbitrary numbers 566, 877, 34 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.