Highest Common Factor of 474, 717, 478 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 474, 717, 478 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 474, 717, 478 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 474, 717, 478 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 474, 717, 478 is 1.

HCF(474, 717, 478) = 1

HCF of 474, 717, 478 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 474, 717, 478 is 1.

Highest Common Factor of 474,717,478 using Euclid's algorithm

Highest Common Factor of 474,717,478 is 1

Step 1: Since 717 > 474, we apply the division lemma to 717 and 474, to get

717 = 474 x 1 + 243

Step 2: Since the reminder 474 ≠ 0, we apply division lemma to 243 and 474, to get

474 = 243 x 1 + 231

Step 3: We consider the new divisor 243 and the new remainder 231, and apply the division lemma to get

243 = 231 x 1 + 12

We consider the new divisor 231 and the new remainder 12,and apply the division lemma to get

231 = 12 x 19 + 3

We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get

12 = 3 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 474 and 717 is 3

Notice that 3 = HCF(12,3) = HCF(231,12) = HCF(243,231) = HCF(474,243) = HCF(717,474) .

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

Step 1: Since 478 > 3, we apply the division lemma to 478 and 3, to get

478 = 3 x 159 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, 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 3 and 478 is 1

Notice that 1 = HCF(3,1) = HCF(478,3) .

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Frequently Asked Questions on HCF of 474, 717, 478 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 474, 717, 478?

Answer: HCF of 474, 717, 478 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 474, 717, 478 using Euclid's Algorithm?

Answer: For arbitrary numbers 474, 717, 478 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.