Highest Common Factor of 961, 580 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 961, 580 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 961, 580 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 961, 580 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 961, 580 is 1.

HCF(961, 580) = 1

HCF of 961, 580 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 961, 580 is 1.

Highest Common Factor of 961,580 using Euclid's algorithm

Highest Common Factor of 961,580 is 1

Step 1: Since 961 > 580, we apply the division lemma to 961 and 580, to get

961 = 580 x 1 + 381

Step 2: Since the reminder 580 ≠ 0, we apply division lemma to 381 and 580, to get

580 = 381 x 1 + 199

Step 3: We consider the new divisor 381 and the new remainder 199, and apply the division lemma to get

381 = 199 x 1 + 182

We consider the new divisor 199 and the new remainder 182,and apply the division lemma to get

199 = 182 x 1 + 17

We consider the new divisor 182 and the new remainder 17,and apply the division lemma to get

182 = 17 x 10 + 12

We consider the new divisor 17 and the new remainder 12,and apply the division lemma to get

17 = 12 x 1 + 5

We consider the new divisor 12 and the new remainder 5,and apply the division lemma to get

12 = 5 x 2 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 961 and 580 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(17,12) = HCF(182,17) = HCF(199,182) = HCF(381,199) = HCF(580,381) = HCF(961,580) .

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Frequently Asked Questions on HCF of 961, 580 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 961, 580?

Answer: HCF of 961, 580 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 961, 580 using Euclid's Algorithm?

Answer: For arbitrary numbers 961, 580 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.