Highest Common Factor of 267, 209, 914 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 267, 209, 914 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 267, 209, 914 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 267, 209, 914 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 267, 209, 914 is 1.

HCF(267, 209, 914) = 1

HCF of 267, 209, 914 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 267, 209, 914 is 1.

Highest Common Factor of 267,209,914 using Euclid's algorithm

Highest Common Factor of 267,209,914 is 1

Step 1: Since 267 > 209, we apply the division lemma to 267 and 209, to get

267 = 209 x 1 + 58

Step 2: Since the reminder 209 ≠ 0, we apply division lemma to 58 and 209, to get

209 = 58 x 3 + 35

Step 3: We consider the new divisor 58 and the new remainder 35, and apply the division lemma to get

58 = 35 x 1 + 23

We consider the new divisor 35 and the new remainder 23,and apply the division lemma to get

35 = 23 x 1 + 12

We consider the new divisor 23 and the new remainder 12,and apply the division lemma to get

23 = 12 x 1 + 11

We consider the new divisor 12 and the new remainder 11,and apply the division lemma to get

12 = 11 x 1 + 1

We consider the new divisor 11 and the new remainder 1,and apply the division lemma to get

11 = 1 x 11 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 267 and 209 is 1

Notice that 1 = HCF(11,1) = HCF(12,11) = HCF(23,12) = HCF(35,23) = HCF(58,35) = HCF(209,58) = HCF(267,209) .

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

Step 1: Since 914 > 1, we apply the division lemma to 914 and 1, to get

914 = 1 x 914 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 914 is 1

Notice that 1 = HCF(914,1) .

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Frequently Asked Questions on HCF of 267, 209, 914 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 267, 209, 914?

Answer: HCF of 267, 209, 914 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 267, 209, 914 using Euclid's Algorithm?

Answer: For arbitrary numbers 267, 209, 914 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.