Highest Common Factor of 2165, 5884 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 2165, 5884 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2165, 5884 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 2165, 5884 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 2165, 5884 is 1.

HCF(2165, 5884) = 1

HCF of 2165, 5884 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 2165, 5884 is 1.

Highest Common Factor of 2165,5884 using Euclid's algorithm

Highest Common Factor of 2165,5884 is 1

Step 1: Since 5884 > 2165, we apply the division lemma to 5884 and 2165, to get

5884 = 2165 x 2 + 1554

Step 2: Since the reminder 2165 ≠ 0, we apply division lemma to 1554 and 2165, to get

2165 = 1554 x 1 + 611

Step 3: We consider the new divisor 1554 and the new remainder 611, and apply the division lemma to get

1554 = 611 x 2 + 332

We consider the new divisor 611 and the new remainder 332,and apply the division lemma to get

611 = 332 x 1 + 279

We consider the new divisor 332 and the new remainder 279,and apply the division lemma to get

332 = 279 x 1 + 53

We consider the new divisor 279 and the new remainder 53,and apply the division lemma to get

279 = 53 x 5 + 14

We consider the new divisor 53 and the new remainder 14,and apply the division lemma to get

53 = 14 x 3 + 11

We consider the new divisor 14 and the new remainder 11,and apply the division lemma to get

14 = 11 x 1 + 3

We consider the new divisor 11 and the new remainder 3,and apply the division lemma to get

11 = 3 x 3 + 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 2165 and 5884 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(53,14) = HCF(279,53) = HCF(332,279) = HCF(611,332) = HCF(1554,611) = HCF(2165,1554) = HCF(5884,2165) .

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Frequently Asked Questions on HCF of 2165, 5884 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 2165, 5884?

Answer: HCF of 2165, 5884 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2165, 5884 using Euclid's Algorithm?

Answer: For arbitrary numbers 2165, 5884 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.