Highest Common Factor of 646, 391, 14 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 646, 391, 14 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 646, 391, 14 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 646, 391, 14 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 646, 391, 14 is 1.

HCF(646, 391, 14) = 1

HCF of 646, 391, 14 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 646, 391, 14 is 1.

Highest Common Factor of 646,391,14 using Euclid's algorithm

Highest Common Factor of 646,391,14 is 1

Step 1: Since 646 > 391, we apply the division lemma to 646 and 391, to get

646 = 391 x 1 + 255

Step 2: Since the reminder 391 ≠ 0, we apply division lemma to 255 and 391, to get

391 = 255 x 1 + 136

Step 3: We consider the new divisor 255 and the new remainder 136, and apply the division lemma to get

255 = 136 x 1 + 119

We consider the new divisor 136 and the new remainder 119,and apply the division lemma to get

136 = 119 x 1 + 17

We consider the new divisor 119 and the new remainder 17,and apply the division lemma to get

119 = 17 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 17, the HCF of 646 and 391 is 17

Notice that 17 = HCF(119,17) = HCF(136,119) = HCF(255,136) = HCF(391,255) = HCF(646,391) .

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

Step 1: Since 17 > 14, we apply the division lemma to 17 and 14, to get

17 = 14 x 1 + 3

Step 2: Since the reminder 14 ≠ 0, we apply division lemma to 3 and 14, to get

14 = 3 x 4 + 2

Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get

3 = 2 x 1 + 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 17 and 14 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(14,3) = HCF(17,14) .

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Frequently Asked Questions on HCF of 646, 391, 14 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 646, 391, 14?

Answer: HCF of 646, 391, 14 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 646, 391, 14 using Euclid's Algorithm?

Answer: For arbitrary numbers 646, 391, 14 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.