Highest Common Factor of 349, 677, 126 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 349, 677, 126 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 349, 677, 126 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 349, 677, 126 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 349, 677, 126 is 1.

HCF(349, 677, 126) = 1

HCF of 349, 677, 126 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 349, 677, 126 is 1.

Highest Common Factor of 349,677,126 using Euclid's algorithm

Highest Common Factor of 349,677,126 is 1

Step 1: Since 677 > 349, we apply the division lemma to 677 and 349, to get

677 = 349 x 1 + 328

Step 2: Since the reminder 349 ≠ 0, we apply division lemma to 328 and 349, to get

349 = 328 x 1 + 21

Step 3: We consider the new divisor 328 and the new remainder 21, and apply the division lemma to get

328 = 21 x 15 + 13

We consider the new divisor 21 and the new remainder 13,and apply the division lemma to get

21 = 13 x 1 + 8

We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get

13 = 8 x 1 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

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 349 and 677 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(21,13) = HCF(328,21) = HCF(349,328) = HCF(677,349) .

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

Step 1: Since 126 > 1, we apply the division lemma to 126 and 1, to get

126 = 1 x 126 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 126 is 1

Notice that 1 = HCF(126,1) .

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Frequently Asked Questions on HCF of 349, 677, 126 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 349, 677, 126?

Answer: HCF of 349, 677, 126 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 349, 677, 126 using Euclid's Algorithm?

Answer: For arbitrary numbers 349, 677, 126 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.