Highest Common Factor of 840, 349, 646 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 840, 349, 646 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 840, 349, 646 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 840, 349, 646 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 840, 349, 646 is 1.

HCF(840, 349, 646) = 1

HCF of 840, 349, 646 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 840, 349, 646 is 1.

Highest Common Factor of 840,349,646 using Euclid's algorithm

Highest Common Factor of 840,349,646 is 1

Step 1: Since 840 > 349, we apply the division lemma to 840 and 349, to get

840 = 349 x 2 + 142

Step 2: Since the reminder 349 ≠ 0, we apply division lemma to 142 and 349, to get

349 = 142 x 2 + 65

Step 3: We consider the new divisor 142 and the new remainder 65, and apply the division lemma to get

142 = 65 x 2 + 12

We consider the new divisor 65 and the new remainder 12,and apply the division lemma to get

65 = 12 x 5 + 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 840 and 349 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(12,5) = HCF(65,12) = HCF(142,65) = HCF(349,142) = HCF(840,349) .

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

Step 1: Since 646 > 1, we apply the division lemma to 646 and 1, to get

646 = 1 x 646 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 646 is 1

Notice that 1 = HCF(646,1) .

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Frequently Asked Questions on HCF of 840, 349, 646 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 840, 349, 646?

Answer: HCF of 840, 349, 646 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 840, 349, 646 using Euclid's Algorithm?

Answer: For arbitrary numbers 840, 349, 646 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.