Highest Common Factor of 422, 611, 408, 166 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 422, 611, 408, 166 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 422, 611, 408, 166 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 422, 611, 408, 166 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 422, 611, 408, 166 is 1.

HCF(422, 611, 408, 166) = 1

HCF of 422, 611, 408, 166 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 422, 611, 408, 166 is 1.

Highest Common Factor of 422,611,408,166 using Euclid's algorithm

Highest Common Factor of 422,611,408,166 is 1

Step 1: Since 611 > 422, we apply the division lemma to 611 and 422, to get

611 = 422 x 1 + 189

Step 2: Since the reminder 422 ≠ 0, we apply division lemma to 189 and 422, to get

422 = 189 x 2 + 44

Step 3: We consider the new divisor 189 and the new remainder 44, and apply the division lemma to get

189 = 44 x 4 + 13

We consider the new divisor 44 and the new remainder 13,and apply the division lemma to get

44 = 13 x 3 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 422 and 611 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(44,13) = HCF(189,44) = HCF(422,189) = HCF(611,422) .

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

Step 1: Since 408 > 1, we apply the division lemma to 408 and 1, to get

408 = 1 x 408 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 408 is 1

Notice that 1 = HCF(408,1) .

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

Step 1: Since 166 > 1, we apply the division lemma to 166 and 1, to get

166 = 1 x 166 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 166 is 1

Notice that 1 = HCF(166,1) .

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Frequently Asked Questions on HCF of 422, 611, 408, 166 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 422, 611, 408, 166?

Answer: HCF of 422, 611, 408, 166 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 422, 611, 408, 166 using Euclid's Algorithm?

Answer: For arbitrary numbers 422, 611, 408, 166 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.