Highest Common Factor of 478, 755, 52 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, 755, 52 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 478, 755, 52 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, 755, 52 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, 755, 52 is 1.

HCF(478, 755, 52) = 1

HCF of 478, 755, 52 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, 755, 52 is 1.

Highest Common Factor of 478,755,52 using Euclid's algorithm

Highest Common Factor of 478,755,52 is 1

Step 1: Since 755 > 478, we apply the division lemma to 755 and 478, to get

755 = 478 x 1 + 277

Step 2: Since the reminder 478 ≠ 0, we apply division lemma to 277 and 478, to get

478 = 277 x 1 + 201

Step 3: We consider the new divisor 277 and the new remainder 201, and apply the division lemma to get

277 = 201 x 1 + 76

We consider the new divisor 201 and the new remainder 76,and apply the division lemma to get

201 = 76 x 2 + 49

We consider the new divisor 76 and the new remainder 49,and apply the division lemma to get

76 = 49 x 1 + 27

We consider the new divisor 49 and the new remainder 27,and apply the division lemma to get

49 = 27 x 1 + 22

We consider the new divisor 27 and the new remainder 22,and apply the division lemma to get

27 = 22 x 1 + 5

We consider the new divisor 22 and the new remainder 5,and apply the division lemma to get

22 = 5 x 4 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 755 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(22,5) = HCF(27,22) = HCF(49,27) = HCF(76,49) = HCF(201,76) = HCF(277,201) = HCF(478,277) = HCF(755,478) .

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

Step 1: Since 52 > 1, we apply the division lemma to 52 and 1, to get

52 = 1 x 52 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 52 is 1

Notice that 1 = HCF(52,1) .

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Frequently Asked Questions on HCF of 478, 755, 52 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, 755, 52?

Answer: HCF of 478, 755, 52 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 478, 755, 52 using Euclid's Algorithm?

Answer: For arbitrary numbers 478, 755, 52 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.