Highest Common Factor of 421, 681, 198 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 421, 681, 198 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 421, 681, 198 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 421, 681, 198 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 421, 681, 198 is 1.

HCF(421, 681, 198) = 1

HCF of 421, 681, 198 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 421, 681, 198 is 1.

Highest Common Factor of 421,681,198 using Euclid's algorithm

Highest Common Factor of 421,681,198 is 1

Step 1: Since 681 > 421, we apply the division lemma to 681 and 421, to get

681 = 421 x 1 + 260

Step 2: Since the reminder 421 ≠ 0, we apply division lemma to 260 and 421, to get

421 = 260 x 1 + 161

Step 3: We consider the new divisor 260 and the new remainder 161, and apply the division lemma to get

260 = 161 x 1 + 99

We consider the new divisor 161 and the new remainder 99,and apply the division lemma to get

161 = 99 x 1 + 62

We consider the new divisor 99 and the new remainder 62,and apply the division lemma to get

99 = 62 x 1 + 37

We consider the new divisor 62 and the new remainder 37,and apply the division lemma to get

62 = 37 x 1 + 25

We consider the new divisor 37 and the new remainder 25,and apply the division lemma to get

37 = 25 x 1 + 12

We consider the new divisor 25 and the new remainder 12,and apply the division lemma to get

25 = 12 x 2 + 1

We consider the new divisor 12 and the new remainder 1,and apply the division lemma to get

12 = 1 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 421 and 681 is 1

Notice that 1 = HCF(12,1) = HCF(25,12) = HCF(37,25) = HCF(62,37) = HCF(99,62) = HCF(161,99) = HCF(260,161) = HCF(421,260) = HCF(681,421) .

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

Step 1: Since 198 > 1, we apply the division lemma to 198 and 1, to get

198 = 1 x 198 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 198 is 1

Notice that 1 = HCF(198,1) .

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Frequently Asked Questions on HCF of 421, 681, 198 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 421, 681, 198?

Answer: HCF of 421, 681, 198 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 421, 681, 198 using Euclid's Algorithm?

Answer: For arbitrary numbers 421, 681, 198 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.