Highest Common Factor of 684, 382, 368 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 684, 382, 368 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 684, 382, 368 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 684, 382, 368 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 684, 382, 368 is 2.

HCF(684, 382, 368) = 2

HCF of 684, 382, 368 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 684, 382, 368 is 2.

Highest Common Factor of 684,382,368 using Euclid's algorithm

Highest Common Factor of 684,382,368 is 2

Step 1: Since 684 > 382, we apply the division lemma to 684 and 382, to get

684 = 382 x 1 + 302

Step 2: Since the reminder 382 ≠ 0, we apply division lemma to 302 and 382, to get

382 = 302 x 1 + 80

Step 3: We consider the new divisor 302 and the new remainder 80, and apply the division lemma to get

302 = 80 x 3 + 62

We consider the new divisor 80 and the new remainder 62,and apply the division lemma to get

80 = 62 x 1 + 18

We consider the new divisor 62 and the new remainder 18,and apply the division lemma to get

62 = 18 x 3 + 8

We consider the new divisor 18 and the new remainder 8,and apply the division lemma to get

18 = 8 x 2 + 2

We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 684 and 382 is 2

Notice that 2 = HCF(8,2) = HCF(18,8) = HCF(62,18) = HCF(80,62) = HCF(302,80) = HCF(382,302) = HCF(684,382) .

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

Step 1: Since 368 > 2, we apply the division lemma to 368 and 2, to get

368 = 2 x 184 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 368 is 2

Notice that 2 = HCF(368,2) .

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Frequently Asked Questions on HCF of 684, 382, 368 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 684, 382, 368?

Answer: HCF of 684, 382, 368 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 684, 382, 368 using Euclid's Algorithm?

Answer: For arbitrary numbers 684, 382, 368 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.