Highest Common Factor of 1999, 5704 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 1999, 5704 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1999, 5704 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 1999, 5704 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 1999, 5704 is 1.

HCF(1999, 5704) = 1

HCF of 1999, 5704 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 1999, 5704 is 1.

Highest Common Factor of 1999,5704 using Euclid's algorithm

Highest Common Factor of 1999,5704 is 1

Step 1: Since 5704 > 1999, we apply the division lemma to 5704 and 1999, to get

5704 = 1999 x 2 + 1706

Step 2: Since the reminder 1999 ≠ 0, we apply division lemma to 1706 and 1999, to get

1999 = 1706 x 1 + 293

Step 3: We consider the new divisor 1706 and the new remainder 293, and apply the division lemma to get

1706 = 293 x 5 + 241

We consider the new divisor 293 and the new remainder 241,and apply the division lemma to get

293 = 241 x 1 + 52

We consider the new divisor 241 and the new remainder 52,and apply the division lemma to get

241 = 52 x 4 + 33

We consider the new divisor 52 and the new remainder 33,and apply the division lemma to get

52 = 33 x 1 + 19

We consider the new divisor 33 and the new remainder 19,and apply the division lemma to get

33 = 19 x 1 + 14

We consider the new divisor 19 and the new remainder 14,and apply the division lemma to get

19 = 14 x 1 + 5

We consider the new divisor 14 and the new remainder 5,and apply the division lemma to get

14 = 5 x 2 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1999 and 5704 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(14,5) = HCF(19,14) = HCF(33,19) = HCF(52,33) = HCF(241,52) = HCF(293,241) = HCF(1706,293) = HCF(1999,1706) = HCF(5704,1999) .

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Frequently Asked Questions on HCF of 1999, 5704 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 1999, 5704?

Answer: HCF of 1999, 5704 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1999, 5704 using Euclid's Algorithm?

Answer: For arbitrary numbers 1999, 5704 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.