Highest Common Factor of 566, 960, 240 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, 960, 240 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 566, 960, 240 is 2 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, 960, 240 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, 960, 240 is 2.

HCF(566, 960, 240) = 2

HCF of 566, 960, 240 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, 960, 240 is 2.

Highest Common Factor of 566,960,240 using Euclid's algorithm

Highest Common Factor of 566,960,240 is 2

Step 1: Since 960 > 566, we apply the division lemma to 960 and 566, to get

960 = 566 x 1 + 394

Step 2: Since the reminder 566 ≠ 0, we apply division lemma to 394 and 566, to get

566 = 394 x 1 + 172

Step 3: We consider the new divisor 394 and the new remainder 172, and apply the division lemma to get

394 = 172 x 2 + 50

We consider the new divisor 172 and the new remainder 50,and apply the division lemma to get

172 = 50 x 3 + 22

We consider the new divisor 50 and the new remainder 22,and apply the division lemma to get

50 = 22 x 2 + 6

We consider the new divisor 22 and the new remainder 6,and apply the division lemma to get

22 = 6 x 3 + 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 960 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(22,6) = HCF(50,22) = HCF(172,50) = HCF(394,172) = HCF(566,394) = HCF(960,566) .

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

Step 1: Since 240 > 2, we apply the division lemma to 240 and 2, to get

240 = 2 x 120 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 240 is 2

Notice that 2 = HCF(240,2) .

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Frequently Asked Questions on HCF of 566, 960, 240 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, 960, 240?

Answer: HCF of 566, 960, 240 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 566, 960, 240 using Euclid's Algorithm?

Answer: For arbitrary numbers 566, 960, 240 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.