Highest Common Factor of 582, 370, 422 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, 370, 422 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 582, 370, 422 is 2 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, 370, 422 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, 370, 422 is 2.

HCF(582, 370, 422) = 2

HCF of 582, 370, 422 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, 370, 422 is 2.

Highest Common Factor of 582,370,422 using Euclid's algorithm

Highest Common Factor of 582,370,422 is 2

Step 1: Since 582 > 370, we apply the division lemma to 582 and 370, to get

582 = 370 x 1 + 212

Step 2: Since the reminder 370 ≠ 0, we apply division lemma to 212 and 370, to get

370 = 212 x 1 + 158

Step 3: We consider the new divisor 212 and the new remainder 158, and apply the division lemma to get

212 = 158 x 1 + 54

We consider the new divisor 158 and the new remainder 54,and apply the division lemma to get

158 = 54 x 2 + 50

We consider the new divisor 54 and the new remainder 50,and apply the division lemma to get

54 = 50 x 1 + 4

We consider the new divisor 50 and the new remainder 4,and apply the division lemma to get

50 = 4 x 12 + 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 370 is 2

Notice that 2 = HCF(4,2) = HCF(50,4) = HCF(54,50) = HCF(158,54) = HCF(212,158) = HCF(370,212) = HCF(582,370) .

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

Step 1: Since 422 > 2, we apply the division lemma to 422 and 2, to get

422 = 2 x 211 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 2 and 422 is 2

Notice that 2 = HCF(422,2) .

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Frequently Asked Questions on HCF of 582, 370, 422 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, 370, 422?

Answer: HCF of 582, 370, 422 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 582, 370, 422 using Euclid's Algorithm?

Answer: For arbitrary numbers 582, 370, 422 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.