Highest Common Factor of 564, 866, 501 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 564, 866, 501 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 564, 866, 501 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 564, 866, 501 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 564, 866, 501 is 1.

HCF(564, 866, 501) = 1

HCF of 564, 866, 501 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 564, 866, 501 is 1.

Highest Common Factor of 564,866,501 using Euclid's algorithm

Highest Common Factor of 564,866,501 is 1

Step 1: Since 866 > 564, we apply the division lemma to 866 and 564, to get

866 = 564 x 1 + 302

Step 2: Since the reminder 564 ≠ 0, we apply division lemma to 302 and 564, to get

564 = 302 x 1 + 262

Step 3: We consider the new divisor 302 and the new remainder 262, and apply the division lemma to get

302 = 262 x 1 + 40

We consider the new divisor 262 and the new remainder 40,and apply the division lemma to get

262 = 40 x 6 + 22

We consider the new divisor 40 and the new remainder 22,and apply the division lemma to get

40 = 22 x 1 + 18

We consider the new divisor 22 and the new remainder 18,and apply the division lemma to get

22 = 18 x 1 + 4

We consider the new divisor 18 and the new remainder 4,and apply the division lemma to get

18 = 4 x 4 + 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 564 and 866 is 2

Notice that 2 = HCF(4,2) = HCF(18,4) = HCF(22,18) = HCF(40,22) = HCF(262,40) = HCF(302,262) = HCF(564,302) = HCF(866,564) .

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

Step 1: Since 501 > 2, we apply the division lemma to 501 and 2, to get

501 = 2 x 250 + 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 501 is 1

Notice that 1 = HCF(2,1) = HCF(501,2) .

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Frequently Asked Questions on HCF of 564, 866, 501 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 564, 866, 501?

Answer: HCF of 564, 866, 501 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 564, 866, 501 using Euclid's Algorithm?

Answer: For arbitrary numbers 564, 866, 501 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.