Highest Common Factor of 87, 312, 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 87, 312, 212 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 87, 312, 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 87, 312, 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 87, 312, 212 is 1.

HCF(87, 312, 212) = 1

HCF of 87, 312, 212 using Euclid's algorithm

Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.

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Highest common factor (HCF) of 87, 312, 212 is 1.

Highest Common Factor of 87,312,212 using Euclid's algorithm

Highest Common Factor of 87,312,212 is 1

Step 1: Since 312 > 87, we apply the division lemma to 312 and 87, to get

312 = 87 x 3 + 51

Step 2: Since the reminder 87 ≠ 0, we apply division lemma to 51 and 87, to get

87 = 51 x 1 + 36

Step 3: We consider the new divisor 51 and the new remainder 36, and apply the division lemma to get

51 = 36 x 1 + 15

We consider the new divisor 36 and the new remainder 15,and apply the division lemma to get

36 = 15 x 2 + 6

We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get

15 = 6 x 2 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 87 and 312 is 3

Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(36,15) = HCF(51,36) = HCF(87,51) = HCF(312,87) .

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 87, 312, 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 87, 312, 212?

Answer: HCF of 87, 312, 212 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 87, 312, 212 using Euclid's Algorithm?

Answer: For arbitrary numbers 87, 312, 212 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.