Highest Common Factor of 566, 964, 923 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, 964, 923 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 566, 964, 923 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, 964, 923 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, 964, 923 is 1.

HCF(566, 964, 923) = 1

HCF of 566, 964, 923 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, 964, 923 is 1.

Highest Common Factor of 566,964,923 using Euclid's algorithm

Highest Common Factor of 566,964,923 is 1

Step 1: Since 964 > 566, we apply the division lemma to 964 and 566, to get

964 = 566 x 1 + 398

Step 2: Since the reminder 566 ≠ 0, we apply division lemma to 398 and 566, to get

566 = 398 x 1 + 168

Step 3: We consider the new divisor 398 and the new remainder 168, and apply the division lemma to get

398 = 168 x 2 + 62

We consider the new divisor 168 and the new remainder 62,and apply the division lemma to get

168 = 62 x 2 + 44

We consider the new divisor 62 and the new remainder 44,and apply the division lemma to get

62 = 44 x 1 + 18

We consider the new divisor 44 and the new remainder 18,and apply the division lemma to get

44 = 18 x 2 + 8

We consider the new divisor 18 and the new remainder 8,and apply the division lemma to get

18 = 8 x 2 + 2

We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 566 and 964 is 2

Notice that 2 = HCF(8,2) = HCF(18,8) = HCF(44,18) = HCF(62,44) = HCF(168,62) = HCF(398,168) = HCF(566,398) = HCF(964,566) .

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

Step 1: Since 923 > 2, we apply the division lemma to 923 and 2, to get

923 = 2 x 461 + 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 923 is 1

Notice that 1 = HCF(2,1) = HCF(923,2) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 566, 964, 923 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, 964, 923?

Answer: HCF of 566, 964, 923 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 566, 964, 923 using Euclid's Algorithm?

Answer: For arbitrary numbers 566, 964, 923 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.