Highest Common Factor of 422, 888, 129 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, 888, 129 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 422, 888, 129 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, 888, 129 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, 888, 129 is 1.

HCF(422, 888, 129) = 1

HCF of 422, 888, 129 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, 888, 129 is 1.

Highest Common Factor of 422,888,129 using Euclid's algorithm

Highest Common Factor of 422,888,129 is 1

Step 1: Since 888 > 422, we apply the division lemma to 888 and 422, to get

888 = 422 x 2 + 44

Step 2: Since the reminder 422 ≠ 0, we apply division lemma to 44 and 422, to get

422 = 44 x 9 + 26

Step 3: We consider the new divisor 44 and the new remainder 26, and apply the division lemma to get

44 = 26 x 1 + 18

We consider the new divisor 26 and the new remainder 18,and apply the division lemma to get

26 = 18 x 1 + 8

We consider the new divisor 18 and the new remainder 8,and apply the division lemma to get

18 = 8 x 2 + 2

We consider the new divisor 8 and the new remainder 2,and apply the division lemma to get

8 = 2 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 422 and 888 is 2

Notice that 2 = HCF(8,2) = HCF(18,8) = HCF(26,18) = HCF(44,26) = HCF(422,44) = HCF(888,422) .

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

Step 1: Since 129 > 2, we apply the division lemma to 129 and 2, to get

129 = 2 x 64 + 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 129 is 1

Notice that 1 = HCF(2,1) = HCF(129,2) .

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Frequently Asked Questions on HCF of 422, 888, 129 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, 888, 129?

Answer: HCF of 422, 888, 129 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 422, 888, 129 using Euclid's Algorithm?

Answer: For arbitrary numbers 422, 888, 129 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.