Highest Common Factor of 1849, 7021, 67009 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 1849, 7021, 67009 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1849, 7021, 67009 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 1849, 7021, 67009 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 1849, 7021, 67009 is 1.

HCF(1849, 7021, 67009) = 1

HCF of 1849, 7021, 67009 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 1849, 7021, 67009 is 1.

Highest Common Factor of 1849,7021,67009 using Euclid's algorithm

Highest Common Factor of 1849,7021,67009 is 1

Step 1: Since 7021 > 1849, we apply the division lemma to 7021 and 1849, to get

7021 = 1849 x 3 + 1474

Step 2: Since the reminder 1849 ≠ 0, we apply division lemma to 1474 and 1849, to get

1849 = 1474 x 1 + 375

Step 3: We consider the new divisor 1474 and the new remainder 375, and apply the division lemma to get

1474 = 375 x 3 + 349

We consider the new divisor 375 and the new remainder 349,and apply the division lemma to get

375 = 349 x 1 + 26

We consider the new divisor 349 and the new remainder 26,and apply the division lemma to get

349 = 26 x 13 + 11

We consider the new divisor 26 and the new remainder 11,and apply the division lemma to get

26 = 11 x 2 + 4

We consider the new divisor 11 and the new remainder 4,and apply the division lemma to get

11 = 4 x 2 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1849 and 7021 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(11,4) = HCF(26,11) = HCF(349,26) = HCF(375,349) = HCF(1474,375) = HCF(1849,1474) = HCF(7021,1849) .

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

Step 1: Since 67009 > 1, we apply the division lemma to 67009 and 1, to get

67009 = 1 x 67009 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 67009 is 1

Notice that 1 = HCF(67009,1) .

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Frequently Asked Questions on HCF of 1849, 7021, 67009 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 1849, 7021, 67009?

Answer: HCF of 1849, 7021, 67009 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1849, 7021, 67009 using Euclid's Algorithm?

Answer: For arbitrary numbers 1849, 7021, 67009 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.