Highest Common Factor of 212, 469, 608 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 212, 469, 608 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 212, 469, 608 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 212, 469, 608 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 212, 469, 608 is 1.

HCF(212, 469, 608) = 1

HCF of 212, 469, 608 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 212, 469, 608 is 1.

Highest Common Factor of 212,469,608 using Euclid's algorithm

Highest Common Factor of 212,469,608 is 1

Step 1: Since 469 > 212, we apply the division lemma to 469 and 212, to get

469 = 212 x 2 + 45

Step 2: Since the reminder 212 ≠ 0, we apply division lemma to 45 and 212, to get

212 = 45 x 4 + 32

Step 3: We consider the new divisor 45 and the new remainder 32, and apply the division lemma to get

45 = 32 x 1 + 13

We consider the new divisor 32 and the new remainder 13,and apply the division lemma to get

32 = 13 x 2 + 6

We consider the new divisor 13 and the new remainder 6,and apply the division lemma to get

13 = 6 x 2 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 212 and 469 is 1

Notice that 1 = HCF(6,1) = HCF(13,6) = HCF(32,13) = HCF(45,32) = HCF(212,45) = HCF(469,212) .

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

Step 1: Since 608 > 1, we apply the division lemma to 608 and 1, to get

608 = 1 x 608 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 608 is 1

Notice that 1 = HCF(608,1) .

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Frequently Asked Questions on HCF of 212, 469, 608 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 212, 469, 608?

Answer: HCF of 212, 469, 608 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 212, 469, 608 using Euclid's Algorithm?

Answer: For arbitrary numbers 212, 469, 608 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.