Highest Common Factor of 6497, 5140, 21653 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 6497, 5140, 21653 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6497, 5140, 21653 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 6497, 5140, 21653 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 6497, 5140, 21653 is 1.

HCF(6497, 5140, 21653) = 1

HCF of 6497, 5140, 21653 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 6497, 5140, 21653 is 1.

Highest Common Factor of 6497,5140,21653 using Euclid's algorithm

Highest Common Factor of 6497,5140,21653 is 1

Step 1: Since 6497 > 5140, we apply the division lemma to 6497 and 5140, to get

6497 = 5140 x 1 + 1357

Step 2: Since the reminder 5140 ≠ 0, we apply division lemma to 1357 and 5140, to get

5140 = 1357 x 3 + 1069

Step 3: We consider the new divisor 1357 and the new remainder 1069, and apply the division lemma to get

1357 = 1069 x 1 + 288

We consider the new divisor 1069 and the new remainder 288,and apply the division lemma to get

1069 = 288 x 3 + 205

We consider the new divisor 288 and the new remainder 205,and apply the division lemma to get

288 = 205 x 1 + 83

We consider the new divisor 205 and the new remainder 83,and apply the division lemma to get

205 = 83 x 2 + 39

We consider the new divisor 83 and the new remainder 39,and apply the division lemma to get

83 = 39 x 2 + 5

We consider the new divisor 39 and the new remainder 5,and apply the division lemma to get

39 = 5 x 7 + 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 6497 and 5140 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(39,5) = HCF(83,39) = HCF(205,83) = HCF(288,205) = HCF(1069,288) = HCF(1357,1069) = HCF(5140,1357) = HCF(6497,5140) .

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

Step 1: Since 21653 > 1, we apply the division lemma to 21653 and 1, to get

21653 = 1 x 21653 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 21653 is 1

Notice that 1 = HCF(21653,1) .

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Frequently Asked Questions on HCF of 6497, 5140, 21653 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 6497, 5140, 21653?

Answer: HCF of 6497, 5140, 21653 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6497, 5140, 21653 using Euclid's Algorithm?

Answer: For arbitrary numbers 6497, 5140, 21653 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.