Highest Common Factor of 212, 998, 469 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, 998, 469 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 212, 998, 469 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, 998, 469 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, 998, 469 is 1.

HCF(212, 998, 469) = 1

HCF of 212, 998, 469 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, 998, 469 is 1.

Highest Common Factor of 212,998,469 using Euclid's algorithm

Highest Common Factor of 212,998,469 is 1

Step 1: Since 998 > 212, we apply the division lemma to 998 and 212, to get

998 = 212 x 4 + 150

Step 2: Since the reminder 212 ≠ 0, we apply division lemma to 150 and 212, to get

212 = 150 x 1 + 62

Step 3: We consider the new divisor 150 and the new remainder 62, and apply the division lemma to get

150 = 62 x 2 + 26

We consider the new divisor 62 and the new remainder 26,and apply the division lemma to get

62 = 26 x 2 + 10

We consider the new divisor 26 and the new remainder 10,and apply the division lemma to get

26 = 10 x 2 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 212 and 998 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(26,10) = HCF(62,26) = HCF(150,62) = HCF(212,150) = HCF(998,212) .

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

Step 1: Since 469 > 2, we apply the division lemma to 469 and 2, to get

469 = 2 x 234 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 469 is 1

Notice that 1 = HCF(2,1) = HCF(469,2) .

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Frequently Asked Questions on HCF of 212, 998, 469 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, 998, 469?

Answer: HCF of 212, 998, 469 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 212, 998, 469 using Euclid's Algorithm?

Answer: For arbitrary numbers 212, 998, 469 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.