Highest Common Factor of 585, 961, 966 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 585, 961, 966 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 585, 961, 966 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 585, 961, 966 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 585, 961, 966 is 1.

HCF(585, 961, 966) = 1

HCF of 585, 961, 966 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 585, 961, 966 is 1.

Highest Common Factor of 585,961,966 using Euclid's algorithm

Highest Common Factor of 585,961,966 is 1

Step 1: Since 961 > 585, we apply the division lemma to 961 and 585, to get

961 = 585 x 1 + 376

Step 2: Since the reminder 585 ≠ 0, we apply division lemma to 376 and 585, to get

585 = 376 x 1 + 209

Step 3: We consider the new divisor 376 and the new remainder 209, and apply the division lemma to get

376 = 209 x 1 + 167

We consider the new divisor 209 and the new remainder 167,and apply the division lemma to get

209 = 167 x 1 + 42

We consider the new divisor 167 and the new remainder 42,and apply the division lemma to get

167 = 42 x 3 + 41

We consider the new divisor 42 and the new remainder 41,and apply the division lemma to get

42 = 41 x 1 + 1

We consider the new divisor 41 and the new remainder 1,and apply the division lemma to get

41 = 1 x 41 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 585 and 961 is 1

Notice that 1 = HCF(41,1) = HCF(42,41) = HCF(167,42) = HCF(209,167) = HCF(376,209) = HCF(585,376) = HCF(961,585) .

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

Step 1: Since 966 > 1, we apply the division lemma to 966 and 1, to get

966 = 1 x 966 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 966 is 1

Notice that 1 = HCF(966,1) .

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Frequently Asked Questions on HCF of 585, 961, 966 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 585, 961, 966?

Answer: HCF of 585, 961, 966 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 585, 961, 966 using Euclid's Algorithm?

Answer: For arbitrary numbers 585, 961, 966 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.