Highest Common Factor of 1267, 2132, 34617 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 1267, 2132, 34617 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1267, 2132, 34617 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 1267, 2132, 34617 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 1267, 2132, 34617 is 1.

HCF(1267, 2132, 34617) = 1

HCF of 1267, 2132, 34617 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 1267, 2132, 34617 is 1.

Highest Common Factor of 1267,2132,34617 using Euclid's algorithm

Highest Common Factor of 1267,2132,34617 is 1

Step 1: Since 2132 > 1267, we apply the division lemma to 2132 and 1267, to get

2132 = 1267 x 1 + 865

Step 2: Since the reminder 1267 ≠ 0, we apply division lemma to 865 and 1267, to get

1267 = 865 x 1 + 402

Step 3: We consider the new divisor 865 and the new remainder 402, and apply the division lemma to get

865 = 402 x 2 + 61

We consider the new divisor 402 and the new remainder 61,and apply the division lemma to get

402 = 61 x 6 + 36

We consider the new divisor 61 and the new remainder 36,and apply the division lemma to get

61 = 36 x 1 + 25

We consider the new divisor 36 and the new remainder 25,and apply the division lemma to get

36 = 25 x 1 + 11

We consider the new divisor 25 and the new remainder 11,and apply the division lemma to get

25 = 11 x 2 + 3

We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get

11 = 3 x 3 + 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 1267 and 2132 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(25,11) = HCF(36,25) = HCF(61,36) = HCF(402,61) = HCF(865,402) = HCF(1267,865) = HCF(2132,1267) .

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

Step 1: Since 34617 > 1, we apply the division lemma to 34617 and 1, to get

34617 = 1 x 34617 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 34617 is 1

Notice that 1 = HCF(34617,1) .

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Frequently Asked Questions on HCF of 1267, 2132, 34617 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 1267, 2132, 34617?

Answer: HCF of 1267, 2132, 34617 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1267, 2132, 34617 using Euclid's Algorithm?

Answer: For arbitrary numbers 1267, 2132, 34617 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.