Highest Common Factor of 580, 360, 524 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 580, 360, 524 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 580, 360, 524 is 4 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 580, 360, 524 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 580, 360, 524 is 4.

HCF(580, 360, 524) = 4

HCF of 580, 360, 524 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 580, 360, 524 is 4.

Highest Common Factor of 580,360,524 using Euclid's algorithm

Highest Common Factor of 580,360,524 is 4

Step 1: Since 580 > 360, we apply the division lemma to 580 and 360, to get

580 = 360 x 1 + 220

Step 2: Since the reminder 360 ≠ 0, we apply division lemma to 220 and 360, to get

360 = 220 x 1 + 140

Step 3: We consider the new divisor 220 and the new remainder 140, and apply the division lemma to get

220 = 140 x 1 + 80

We consider the new divisor 140 and the new remainder 80,and apply the division lemma to get

140 = 80 x 1 + 60

We consider the new divisor 80 and the new remainder 60,and apply the division lemma to get

80 = 60 x 1 + 20

We consider the new divisor 60 and the new remainder 20,and apply the division lemma to get

60 = 20 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 20, the HCF of 580 and 360 is 20

Notice that 20 = HCF(60,20) = HCF(80,60) = HCF(140,80) = HCF(220,140) = HCF(360,220) = HCF(580,360) .

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

Step 1: Since 524 > 20, we apply the division lemma to 524 and 20, to get

524 = 20 x 26 + 4

Step 2: Since the reminder 20 ≠ 0, we apply division lemma to 4 and 20, to get

20 = 4 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 20 and 524 is 4

Notice that 4 = HCF(20,4) = HCF(524,20) .

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Frequently Asked Questions on HCF of 580, 360, 524 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 580, 360, 524?

Answer: HCF of 580, 360, 524 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 580, 360, 524 using Euclid's Algorithm?

Answer: For arbitrary numbers 580, 360, 524 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.