Highest Common Factor of 588, 987, 827 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 588, 987, 827 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 588, 987, 827 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 588, 987, 827 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 588, 987, 827 is 1.

HCF(588, 987, 827) = 1

HCF of 588, 987, 827 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 588, 987, 827 is 1.

Highest Common Factor of 588,987,827 using Euclid's algorithm

Highest Common Factor of 588,987,827 is 1

Step 1: Since 987 > 588, we apply the division lemma to 987 and 588, to get

987 = 588 x 1 + 399

Step 2: Since the reminder 588 ≠ 0, we apply division lemma to 399 and 588, to get

588 = 399 x 1 + 189

Step 3: We consider the new divisor 399 and the new remainder 189, and apply the division lemma to get

399 = 189 x 2 + 21

We consider the new divisor 189 and the new remainder 21, and apply the division lemma to get

189 = 21 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 21, the HCF of 588 and 987 is 21

Notice that 21 = HCF(189,21) = HCF(399,189) = HCF(588,399) = HCF(987,588) .

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

Step 1: Since 827 > 21, we apply the division lemma to 827 and 21, to get

827 = 21 x 39 + 8

Step 2: Since the reminder 21 ≠ 0, we apply division lemma to 8 and 21, to get

21 = 8 x 2 + 5

Step 3: We consider the new divisor 8 and the new remainder 5, and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma 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 21 and 827 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(21,8) = HCF(827,21) .

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Frequently Asked Questions on HCF of 588, 987, 827 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 588, 987, 827?

Answer: HCF of 588, 987, 827 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 588, 987, 827 using Euclid's Algorithm?

Answer: For arbitrary numbers 588, 987, 827 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.