Highest Common Factor of 961, 398, 586, 308 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, 398, 586, 308 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 961, 398, 586, 308 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, 398, 586, 308 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, 398, 586, 308 is 1.

HCF(961, 398, 586, 308) = 1

HCF of 961, 398, 586, 308 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, 398, 586, 308 is 1.

Highest Common Factor of 961,398,586,308 using Euclid's algorithm

Highest Common Factor of 961,398,586,308 is 1

Step 1: Since 961 > 398, we apply the division lemma to 961 and 398, to get

961 = 398 x 2 + 165

Step 2: Since the reminder 398 ≠ 0, we apply division lemma to 165 and 398, to get

398 = 165 x 2 + 68

Step 3: We consider the new divisor 165 and the new remainder 68, and apply the division lemma to get

165 = 68 x 2 + 29

We consider the new divisor 68 and the new remainder 29,and apply the division lemma to get

68 = 29 x 2 + 10

We consider the new divisor 29 and the new remainder 10,and apply the division lemma to get

29 = 10 x 2 + 9

We consider the new divisor 10 and the new remainder 9,and apply the division lemma to get

10 = 9 x 1 + 1

We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get

9 = 1 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 961 and 398 is 1

Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(29,10) = HCF(68,29) = HCF(165,68) = HCF(398,165) = HCF(961,398) .

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

Step 1: Since 586 > 1, we apply the division lemma to 586 and 1, to get

586 = 1 x 586 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 586 is 1

Notice that 1 = HCF(586,1) .

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

Step 1: Since 308 > 1, we apply the division lemma to 308 and 1, to get

308 = 1 x 308 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 308 is 1

Notice that 1 = HCF(308,1) .

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Frequently Asked Questions on HCF of 961, 398, 586, 308 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, 398, 586, 308?

Answer: HCF of 961, 398, 586, 308 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 961, 398, 586, 308 using Euclid's Algorithm?

Answer: For arbitrary numbers 961, 398, 586, 308 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.