Highest Common Factor of 582, 352, 47 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 582, 352, 47 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 582, 352, 47 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 582, 352, 47 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 582, 352, 47 is 1.

HCF(582, 352, 47) = 1

HCF of 582, 352, 47 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 582, 352, 47 is 1.

Highest Common Factor of 582,352,47 using Euclid's algorithm

Highest Common Factor of 582,352,47 is 1

Step 1: Since 582 > 352, we apply the division lemma to 582 and 352, to get

582 = 352 x 1 + 230

Step 2: Since the reminder 352 ≠ 0, we apply division lemma to 230 and 352, to get

352 = 230 x 1 + 122

Step 3: We consider the new divisor 230 and the new remainder 122, and apply the division lemma to get

230 = 122 x 1 + 108

We consider the new divisor 122 and the new remainder 108,and apply the division lemma to get

122 = 108 x 1 + 14

We consider the new divisor 108 and the new remainder 14,and apply the division lemma to get

108 = 14 x 7 + 10

We consider the new divisor 14 and the new remainder 10,and apply the division lemma to get

14 = 10 x 1 + 4

We consider the new divisor 10 and the new remainder 4,and apply the division lemma to get

10 = 4 x 2 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 582 and 352 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(14,10) = HCF(108,14) = HCF(122,108) = HCF(230,122) = HCF(352,230) = HCF(582,352) .

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

Step 1: Since 47 > 2, we apply the division lemma to 47 and 2, to get

47 = 2 x 23 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 47 is 1

Notice that 1 = HCF(2,1) = HCF(47,2) .

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Frequently Asked Questions on HCF of 582, 352, 47 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 582, 352, 47?

Answer: HCF of 582, 352, 47 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 582, 352, 47 using Euclid's Algorithm?

Answer: For arbitrary numbers 582, 352, 47 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.