Highest Common Factor of 478, 8377, 5182 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 478, 8377, 5182 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 478, 8377, 5182 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 478, 8377, 5182 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 478, 8377, 5182 is 1.

HCF(478, 8377, 5182) = 1

HCF of 478, 8377, 5182 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 478, 8377, 5182 is 1.

Highest Common Factor of 478,8377,5182 using Euclid's algorithm

Highest Common Factor of 478,8377,5182 is 1

Step 1: Since 8377 > 478, we apply the division lemma to 8377 and 478, to get

8377 = 478 x 17 + 251

Step 2: Since the reminder 478 ≠ 0, we apply division lemma to 251 and 478, to get

478 = 251 x 1 + 227

Step 3: We consider the new divisor 251 and the new remainder 227, and apply the division lemma to get

251 = 227 x 1 + 24

We consider the new divisor 227 and the new remainder 24,and apply the division lemma to get

227 = 24 x 9 + 11

We consider the new divisor 24 and the new remainder 11,and apply the division lemma to get

24 = 11 x 2 + 2

We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get

11 = 2 x 5 + 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 478 and 8377 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(24,11) = HCF(227,24) = HCF(251,227) = HCF(478,251) = HCF(8377,478) .

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

Step 1: Since 5182 > 1, we apply the division lemma to 5182 and 1, to get

5182 = 1 x 5182 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 5182 is 1

Notice that 1 = HCF(5182,1) .

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Frequently Asked Questions on HCF of 478, 8377, 5182 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 478, 8377, 5182?

Answer: HCF of 478, 8377, 5182 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 478, 8377, 5182 using Euclid's Algorithm?

Answer: For arbitrary numbers 478, 8377, 5182 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.