Highest Common Factor of 310, 860, 584 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 310, 860, 584 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 310, 860, 584 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 310, 860, 584 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 310, 860, 584 is 2.

HCF(310, 860, 584) = 2

HCF of 310, 860, 584 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 310, 860, 584 is 2.

Highest Common Factor of 310,860,584 using Euclid's algorithm

Highest Common Factor of 310,860,584 is 2

Step 1: Since 860 > 310, we apply the division lemma to 860 and 310, to get

860 = 310 x 2 + 240

Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 240 and 310, to get

310 = 240 x 1 + 70

Step 3: We consider the new divisor 240 and the new remainder 70, and apply the division lemma to get

240 = 70 x 3 + 30

We consider the new divisor 70 and the new remainder 30,and apply the division lemma to get

70 = 30 x 2 + 10

We consider the new divisor 30 and the new remainder 10,and apply the division lemma to get

30 = 10 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 10, the HCF of 310 and 860 is 10

Notice that 10 = HCF(30,10) = HCF(70,30) = HCF(240,70) = HCF(310,240) = HCF(860,310) .

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

Step 1: Since 584 > 10, we apply the division lemma to 584 and 10, to get

584 = 10 x 58 + 4

Step 2: Since the reminder 10 ≠ 0, we apply division lemma to 4 and 10, to get

10 = 4 x 2 + 2

Step 3: 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 10 and 584 is 2

Notice that 2 = HCF(4,2) = HCF(10,4) = HCF(584,10) .

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Frequently Asked Questions on HCF of 310, 860, 584 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 310, 860, 584?

Answer: HCF of 310, 860, 584 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 310, 860, 584 using Euclid's Algorithm?

Answer: For arbitrary numbers 310, 860, 584 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.