Highest Common Factor of 508, 828, 588 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 508, 828, 588 i.e. 4 the largest integer that leaves a remainder zero for all numbers.

HCF of 508, 828, 588 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 508, 828, 588 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 508, 828, 588 is 4.

HCF(508, 828, 588) = 4

HCF of 508, 828, 588 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 508, 828, 588 is 4.

Highest Common Factor of 508,828,588 using Euclid's algorithm

Highest Common Factor of 508,828,588 is 4

Step 1: Since 828 > 508, we apply the division lemma to 828 and 508, to get

828 = 508 x 1 + 320

Step 2: Since the reminder 508 ≠ 0, we apply division lemma to 320 and 508, to get

508 = 320 x 1 + 188

Step 3: We consider the new divisor 320 and the new remainder 188, and apply the division lemma to get

320 = 188 x 1 + 132

We consider the new divisor 188 and the new remainder 132,and apply the division lemma to get

188 = 132 x 1 + 56

We consider the new divisor 132 and the new remainder 56,and apply the division lemma to get

132 = 56 x 2 + 20

We consider the new divisor 56 and the new remainder 20,and apply the division lemma to get

56 = 20 x 2 + 16

We consider the new divisor 20 and the new remainder 16,and apply the division lemma to get

20 = 16 x 1 + 4

We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get

16 = 4 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 508 and 828 is 4

Notice that 4 = HCF(16,4) = HCF(20,16) = HCF(56,20) = HCF(132,56) = HCF(188,132) = HCF(320,188) = HCF(508,320) = HCF(828,508) .

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

Step 1: Since 588 > 4, we apply the division lemma to 588 and 4, to get

588 = 4 x 147 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 4 and 588 is 4

Notice that 4 = HCF(588,4) .

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Frequently Asked Questions on HCF of 508, 828, 588 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 508, 828, 588?

Answer: HCF of 508, 828, 588 is 4 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 508, 828, 588 using Euclid's Algorithm?

Answer: For arbitrary numbers 508, 828, 588 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.