Highest Common Factor of 5968, 3274 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 5968, 3274 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 5968, 3274 is 2 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 5968, 3274 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 5968, 3274 is 2.

HCF(5968, 3274) = 2

HCF of 5968, 3274 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 5968, 3274 is 2.

Highest Common Factor of 5968,3274 using Euclid's algorithm

Highest Common Factor of 5968,3274 is 2

Step 1: Since 5968 > 3274, we apply the division lemma to 5968 and 3274, to get

5968 = 3274 x 1 + 2694

Step 2: Since the reminder 3274 ≠ 0, we apply division lemma to 2694 and 3274, to get

3274 = 2694 x 1 + 580

Step 3: We consider the new divisor 2694 and the new remainder 580, and apply the division lemma to get

2694 = 580 x 4 + 374

We consider the new divisor 580 and the new remainder 374,and apply the division lemma to get

580 = 374 x 1 + 206

We consider the new divisor 374 and the new remainder 206,and apply the division lemma to get

374 = 206 x 1 + 168

We consider the new divisor 206 and the new remainder 168,and apply the division lemma to get

206 = 168 x 1 + 38

We consider the new divisor 168 and the new remainder 38,and apply the division lemma to get

168 = 38 x 4 + 16

We consider the new divisor 38 and the new remainder 16,and apply the division lemma to get

38 = 16 x 2 + 6

We consider the new divisor 16 and the new remainder 6,and apply the division lemma to get

16 = 6 x 2 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 5968 and 3274 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(16,6) = HCF(38,16) = HCF(168,38) = HCF(206,168) = HCF(374,206) = HCF(580,374) = HCF(2694,580) = HCF(3274,2694) = HCF(5968,3274) .

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Frequently Asked Questions on HCF of 5968, 3274 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 5968, 3274?

Answer: HCF of 5968, 3274 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 5968, 3274 using Euclid's Algorithm?

Answer: For arbitrary numbers 5968, 3274 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.