Highest Common Factor of 564, 961 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, 961 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 564, 961 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, 961 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, 961 is 1.

HCF(564, 961) = 1

HCF of 564, 961 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, 961 is 1.

Highest Common Factor of 564,961 using Euclid's algorithm

Highest Common Factor of 564,961 is 1

Step 1: Since 961 > 564, we apply the division lemma to 961 and 564, to get

961 = 564 x 1 + 397

Step 2: Since the reminder 564 ≠ 0, we apply division lemma to 397 and 564, to get

564 = 397 x 1 + 167

Step 3: We consider the new divisor 397 and the new remainder 167, and apply the division lemma to get

397 = 167 x 2 + 63

We consider the new divisor 167 and the new remainder 63,and apply the division lemma to get

167 = 63 x 2 + 41

We consider the new divisor 63 and the new remainder 41,and apply the division lemma to get

63 = 41 x 1 + 22

We consider the new divisor 41 and the new remainder 22,and apply the division lemma to get

41 = 22 x 1 + 19

We consider the new divisor 22 and the new remainder 19,and apply the division lemma to get

22 = 19 x 1 + 3

We consider the new divisor 19 and the new remainder 3,and apply the division lemma to get

19 = 3 x 6 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 564 and 961 is 1

Notice that 1 = HCF(3,1) = HCF(19,3) = HCF(22,19) = HCF(41,22) = HCF(63,41) = HCF(167,63) = HCF(397,167) = HCF(564,397) = HCF(961,564) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 564, 961 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, 961?

Answer: HCF of 564, 961 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 564, 961 using Euclid's Algorithm?

Answer: For arbitrary numbers 564, 961 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.