Highest Common Factor of 343, 614, 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 343, 614, 961 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 343, 614, 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 343, 614, 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 343, 614, 961 is 1.

HCF(343, 614, 961) = 1

HCF of 343, 614, 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 343, 614, 961 is 1.

Highest Common Factor of 343,614,961 using Euclid's algorithm

Highest Common Factor of 343,614,961 is 1

Step 1: Since 614 > 343, we apply the division lemma to 614 and 343, to get

614 = 343 x 1 + 271

Step 2: Since the reminder 343 ≠ 0, we apply division lemma to 271 and 343, to get

343 = 271 x 1 + 72

Step 3: We consider the new divisor 271 and the new remainder 72, and apply the division lemma to get

271 = 72 x 3 + 55

We consider the new divisor 72 and the new remainder 55,and apply the division lemma to get

72 = 55 x 1 + 17

We consider the new divisor 55 and the new remainder 17,and apply the division lemma to get

55 = 17 x 3 + 4

We consider the new divisor 17 and the new remainder 4,and apply the division lemma to get

17 = 4 x 4 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 343 and 614 is 1

Notice that 1 = HCF(4,1) = HCF(17,4) = HCF(55,17) = HCF(72,55) = HCF(271,72) = HCF(343,271) = HCF(614,343) .

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

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

961 = 1 x 961 + 0

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

Notice that 1 = HCF(961,1) .

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Frequently Asked Questions on HCF of 343, 614, 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 343, 614, 961?

Answer: HCF of 343, 614, 961 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 343, 614, 961 using Euclid's Algorithm?

Answer: For arbitrary numbers 343, 614, 961 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.