Highest Common Factor of 634, 992, 29 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 634, 992, 29 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 634, 992, 29 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 634, 992, 29 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 634, 992, 29 is 1.

HCF(634, 992, 29) = 1

HCF of 634, 992, 29 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 634, 992, 29 is 1.

Highest Common Factor of 634,992,29 using Euclid's algorithm

Highest Common Factor of 634,992,29 is 1

Step 1: Since 992 > 634, we apply the division lemma to 992 and 634, to get

992 = 634 x 1 + 358

Step 2: Since the reminder 634 ≠ 0, we apply division lemma to 358 and 634, to get

634 = 358 x 1 + 276

Step 3: We consider the new divisor 358 and the new remainder 276, and apply the division lemma to get

358 = 276 x 1 + 82

We consider the new divisor 276 and the new remainder 82,and apply the division lemma to get

276 = 82 x 3 + 30

We consider the new divisor 82 and the new remainder 30,and apply the division lemma to get

82 = 30 x 2 + 22

We consider the new divisor 30 and the new remainder 22,and apply the division lemma to get

30 = 22 x 1 + 8

We consider the new divisor 22 and the new remainder 8,and apply the division lemma to get

22 = 8 x 2 + 6

We consider the new divisor 8 and the new remainder 6,and apply the division lemma to get

8 = 6 x 1 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 634 and 992 is 2

Notice that 2 = HCF(6,2) = HCF(8,6) = HCF(22,8) = HCF(30,22) = HCF(82,30) = HCF(276,82) = HCF(358,276) = HCF(634,358) = HCF(992,634) .

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

Step 1: Since 29 > 2, we apply the division lemma to 29 and 2, to get

29 = 2 x 14 + 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 29 is 1

Notice that 1 = HCF(2,1) = HCF(29,2) .

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Frequently Asked Questions on HCF of 634, 992, 29 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 634, 992, 29?

Answer: HCF of 634, 992, 29 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 634, 992, 29 using Euclid's Algorithm?

Answer: For arbitrary numbers 634, 992, 29 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.