Highest Common Factor of 267, 996, 872 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, 996, 872 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 267, 996, 872 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, 996, 872 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, 996, 872 is 1.

HCF(267, 996, 872) = 1

HCF of 267, 996, 872 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, 996, 872 is 1.

Highest Common Factor of 267,996,872 using Euclid's algorithm

Highest Common Factor of 267,996,872 is 1

Step 1: Since 996 > 267, we apply the division lemma to 996 and 267, to get

996 = 267 x 3 + 195

Step 2: Since the reminder 267 ≠ 0, we apply division lemma to 195 and 267, to get

267 = 195 x 1 + 72

Step 3: We consider the new divisor 195 and the new remainder 72, and apply the division lemma to get

195 = 72 x 2 + 51

We consider the new divisor 72 and the new remainder 51,and apply the division lemma to get

72 = 51 x 1 + 21

We consider the new divisor 51 and the new remainder 21,and apply the division lemma to get

51 = 21 x 2 + 9

We consider the new divisor 21 and the new remainder 9,and apply the division lemma to get

21 = 9 x 2 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 267 and 996 is 3

Notice that 3 = HCF(9,3) = HCF(21,9) = HCF(51,21) = HCF(72,51) = HCF(195,72) = HCF(267,195) = HCF(996,267) .

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

Step 1: Since 872 > 3, we apply the division lemma to 872 and 3, to get

872 = 3 x 290 + 2

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

3 = 2 x 1 + 1

Step 3: 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 3 and 872 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(872,3) .

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Frequently Asked Questions on HCF of 267, 996, 872 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, 996, 872?

Answer: HCF of 267, 996, 872 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 267, 996, 872 using Euclid's Algorithm?

Answer: For arbitrary numbers 267, 996, 872 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.