Highest Common Factor of 867, 735, 212 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 867, 735, 212 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 867, 735, 212 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 867, 735, 212 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 867, 735, 212 is 1.

HCF(867, 735, 212) = 1

HCF of 867, 735, 212 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 867, 735, 212 is 1.

Highest Common Factor of 867,735,212 using Euclid's algorithm

Highest Common Factor of 867,735,212 is 1

Step 1: Since 867 > 735, we apply the division lemma to 867 and 735, to get

867 = 735 x 1 + 132

Step 2: Since the reminder 735 ≠ 0, we apply division lemma to 132 and 735, to get

735 = 132 x 5 + 75

Step 3: We consider the new divisor 132 and the new remainder 75, and apply the division lemma to get

132 = 75 x 1 + 57

We consider the new divisor 75 and the new remainder 57,and apply the division lemma to get

75 = 57 x 1 + 18

We consider the new divisor 57 and the new remainder 18,and apply the division lemma to get

57 = 18 x 3 + 3

We consider the new divisor 18 and the new remainder 3,and apply the division lemma to get

18 = 3 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 867 and 735 is 3

Notice that 3 = HCF(18,3) = HCF(57,18) = HCF(75,57) = HCF(132,75) = HCF(735,132) = HCF(867,735) .

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

Step 1: Since 212 > 3, we apply the division lemma to 212 and 3, to get

212 = 3 x 70 + 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 212 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(212,3) .

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Frequently Asked Questions on HCF of 867, 735, 212 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 867, 735, 212?

Answer: HCF of 867, 735, 212 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 867, 735, 212 using Euclid's Algorithm?

Answer: For arbitrary numbers 867, 735, 212 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.