Highest Common Factor of 267, 700, 396 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, 700, 396 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 267, 700, 396 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, 700, 396 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, 700, 396 is 1.

HCF(267, 700, 396) = 1

HCF of 267, 700, 396 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, 700, 396 is 1.

Highest Common Factor of 267,700,396 using Euclid's algorithm

Highest Common Factor of 267,700,396 is 1

Step 1: Since 700 > 267, we apply the division lemma to 700 and 267, to get

700 = 267 x 2 + 166

Step 2: Since the reminder 267 ≠ 0, we apply division lemma to 166 and 267, to get

267 = 166 x 1 + 101

Step 3: We consider the new divisor 166 and the new remainder 101, and apply the division lemma to get

166 = 101 x 1 + 65

We consider the new divisor 101 and the new remainder 65,and apply the division lemma to get

101 = 65 x 1 + 36

We consider the new divisor 65 and the new remainder 36,and apply the division lemma to get

65 = 36 x 1 + 29

We consider the new divisor 36 and the new remainder 29,and apply the division lemma to get

36 = 29 x 1 + 7

We consider the new divisor 29 and the new remainder 7,and apply the division lemma to get

29 = 7 x 4 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 267 and 700 is 1

Notice that 1 = HCF(7,1) = HCF(29,7) = HCF(36,29) = HCF(65,36) = HCF(101,65) = HCF(166,101) = HCF(267,166) = HCF(700,267) .

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

Step 1: Since 396 > 1, we apply the division lemma to 396 and 1, to get

396 = 1 x 396 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 396 is 1

Notice that 1 = HCF(396,1) .

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Frequently Asked Questions on HCF of 267, 700, 396 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, 700, 396?

Answer: HCF of 267, 700, 396 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 267, 700, 396 using Euclid's Algorithm?

Answer: For arbitrary numbers 267, 700, 396 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.