Highest Common Factor of 5583, 5046, 21857 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 5583, 5046, 21857 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 5583, 5046, 21857 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 5583, 5046, 21857 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 5583, 5046, 21857 is 1.

HCF(5583, 5046, 21857) = 1

HCF of 5583, 5046, 21857 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 5583, 5046, 21857 is 1.

Highest Common Factor of 5583,5046,21857 using Euclid's algorithm

Highest Common Factor of 5583,5046,21857 is 1

Step 1: Since 5583 > 5046, we apply the division lemma to 5583 and 5046, to get

5583 = 5046 x 1 + 537

Step 2: Since the reminder 5046 ≠ 0, we apply division lemma to 537 and 5046, to get

5046 = 537 x 9 + 213

Step 3: We consider the new divisor 537 and the new remainder 213, and apply the division lemma to get

537 = 213 x 2 + 111

We consider the new divisor 213 and the new remainder 111,and apply the division lemma to get

213 = 111 x 1 + 102

We consider the new divisor 111 and the new remainder 102,and apply the division lemma to get

111 = 102 x 1 + 9

We consider the new divisor 102 and the new remainder 9,and apply the division lemma to get

102 = 9 x 11 + 3

We consider the new divisor 9 and the new remainder 3,and apply the division lemma to get

9 = 3 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 5583 and 5046 is 3

Notice that 3 = HCF(9,3) = HCF(102,9) = HCF(111,102) = HCF(213,111) = HCF(537,213) = HCF(5046,537) = HCF(5583,5046) .

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

Step 1: Since 21857 > 3, we apply the division lemma to 21857 and 3, to get

21857 = 3 x 7285 + 2

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 2 and 3, to get

3 = 2 x 1 + 1

Step 3: 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 3 and 21857 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(21857,3) .

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Frequently Asked Questions on HCF of 5583, 5046, 21857 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 5583, 5046, 21857?

Answer: HCF of 5583, 5046, 21857 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 5583, 5046, 21857 using Euclid's Algorithm?

Answer: For arbitrary numbers 5583, 5046, 21857 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.