Highest Common Factor of 6649, 2101, 68003 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 6649, 2101, 68003 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 6649, 2101, 68003 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 6649, 2101, 68003 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 6649, 2101, 68003 is 1.

HCF(6649, 2101, 68003) = 1

HCF of 6649, 2101, 68003 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 6649, 2101, 68003 is 1.

Highest Common Factor of 6649,2101,68003 using Euclid's algorithm

Highest Common Factor of 6649,2101,68003 is 1

Step 1: Since 6649 > 2101, we apply the division lemma to 6649 and 2101, to get

6649 = 2101 x 3 + 346

Step 2: Since the reminder 2101 ≠ 0, we apply division lemma to 346 and 2101, to get

2101 = 346 x 6 + 25

Step 3: We consider the new divisor 346 and the new remainder 25, and apply the division lemma to get

346 = 25 x 13 + 21

We consider the new divisor 25 and the new remainder 21,and apply the division lemma to get

25 = 21 x 1 + 4

We consider the new divisor 21 and the new remainder 4,and apply the division lemma to get

21 = 4 x 5 + 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 6649 and 2101 is 1

Notice that 1 = HCF(4,1) = HCF(21,4) = HCF(25,21) = HCF(346,25) = HCF(2101,346) = HCF(6649,2101) .

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

Step 1: Since 68003 > 1, we apply the division lemma to 68003 and 1, to get

68003 = 1 x 68003 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 68003 is 1

Notice that 1 = HCF(68003,1) .

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Frequently Asked Questions on HCF of 6649, 2101, 68003 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 6649, 2101, 68003?

Answer: HCF of 6649, 2101, 68003 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6649, 2101, 68003 using Euclid's Algorithm?

Answer: For arbitrary numbers 6649, 2101, 68003 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.