Highest Common Factor of 473, 580, 31 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 473, 580, 31 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 473, 580, 31 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 473, 580, 31 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 473, 580, 31 is 1.

HCF(473, 580, 31) = 1

HCF of 473, 580, 31 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 473, 580, 31 is 1.

Highest Common Factor of 473,580,31 using Euclid's algorithm

Highest Common Factor of 473,580,31 is 1

Step 1: Since 580 > 473, we apply the division lemma to 580 and 473, to get

580 = 473 x 1 + 107

Step 2: Since the reminder 473 ≠ 0, we apply division lemma to 107 and 473, to get

473 = 107 x 4 + 45

Step 3: We consider the new divisor 107 and the new remainder 45, and apply the division lemma to get

107 = 45 x 2 + 17

We consider the new divisor 45 and the new remainder 17,and apply the division lemma to get

45 = 17 x 2 + 11

We consider the new divisor 17 and the new remainder 11,and apply the division lemma to get

17 = 11 x 1 + 6

We consider the new divisor 11 and the new remainder 6,and apply the division lemma to get

11 = 6 x 1 + 5

We consider the new divisor 6 and the new remainder 5,and apply the division lemma to get

6 = 5 x 1 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 473 and 580 is 1

Notice that 1 = HCF(5,1) = HCF(6,5) = HCF(11,6) = HCF(17,11) = HCF(45,17) = HCF(107,45) = HCF(473,107) = HCF(580,473) .

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

Step 1: Since 31 > 1, we apply the division lemma to 31 and 1, to get

31 = 1 x 31 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 31 is 1

Notice that 1 = HCF(31,1) .

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Frequently Asked Questions on HCF of 473, 580, 31 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 473, 580, 31?

Answer: HCF of 473, 580, 31 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 473, 580, 31 using Euclid's Algorithm?

Answer: For arbitrary numbers 473, 580, 31 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.