Highest Common Factor of 634, 413, 754 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, 413, 754 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 634, 413, 754 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, 413, 754 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, 413, 754 is 1.

HCF(634, 413, 754) = 1

HCF of 634, 413, 754 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, 413, 754 is 1.

Highest Common Factor of 634,413,754 using Euclid's algorithm

Highest Common Factor of 634,413,754 is 1

Step 1: Since 634 > 413, we apply the division lemma to 634 and 413, to get

634 = 413 x 1 + 221

Step 2: Since the reminder 413 ≠ 0, we apply division lemma to 221 and 413, to get

413 = 221 x 1 + 192

Step 3: We consider the new divisor 221 and the new remainder 192, and apply the division lemma to get

221 = 192 x 1 + 29

We consider the new divisor 192 and the new remainder 29,and apply the division lemma to get

192 = 29 x 6 + 18

We consider the new divisor 29 and the new remainder 18,and apply the division lemma to get

29 = 18 x 1 + 11

We consider the new divisor 18 and the new remainder 11,and apply the division lemma to get

18 = 11 x 1 + 7

We consider the new divisor 11 and the new remainder 7,and apply the division lemma to get

11 = 7 x 1 + 4

We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get

7 = 4 x 1 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 634 and 413 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(18,11) = HCF(29,18) = HCF(192,29) = HCF(221,192) = HCF(413,221) = HCF(634,413) .

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

Step 1: Since 754 > 1, we apply the division lemma to 754 and 1, to get

754 = 1 x 754 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 754 is 1

Notice that 1 = HCF(754,1) .

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Frequently Asked Questions on HCF of 634, 413, 754 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, 413, 754?

Answer: HCF of 634, 413, 754 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 634, 413, 754 using Euclid's Algorithm?

Answer: For arbitrary numbers 634, 413, 754 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.