Highest Common Factor of 642, 377, 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 642, 377, 212 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 642, 377, 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 642, 377, 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 642, 377, 212 is 1.

HCF(642, 377, 212) = 1

HCF of 642, 377, 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 642, 377, 212 is 1.

Highest Common Factor of 642,377,212 using Euclid's algorithm

Highest Common Factor of 642,377,212 is 1

Step 1: Since 642 > 377, we apply the division lemma to 642 and 377, to get

642 = 377 x 1 + 265

Step 2: Since the reminder 377 ≠ 0, we apply division lemma to 265 and 377, to get

377 = 265 x 1 + 112

Step 3: We consider the new divisor 265 and the new remainder 112, and apply the division lemma to get

265 = 112 x 2 + 41

We consider the new divisor 112 and the new remainder 41,and apply the division lemma to get

112 = 41 x 2 + 30

We consider the new divisor 41 and the new remainder 30,and apply the division lemma to get

41 = 30 x 1 + 11

We consider the new divisor 30 and the new remainder 11,and apply the division lemma to get

30 = 11 x 2 + 8

We consider the new divisor 11 and the new remainder 8,and apply the division lemma to get

11 = 8 x 1 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

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 642 and 377 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(11,8) = HCF(30,11) = HCF(41,30) = HCF(112,41) = HCF(265,112) = HCF(377,265) = HCF(642,377) .

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

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

212 = 1 x 212 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 212 is 1

Notice that 1 = HCF(212,1) .

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Frequently Asked Questions on HCF of 642, 377, 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 642, 377, 212?

Answer: HCF of 642, 377, 212 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 642, 377, 212 using Euclid's Algorithm?

Answer: For arbitrary numbers 642, 377, 212 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.