Highest Common Factor of 1691, 8005 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 1691, 8005 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1691, 8005 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 1691, 8005 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 1691, 8005 is 1.

HCF(1691, 8005) = 1

HCF of 1691, 8005 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 1691, 8005 is 1.

Highest Common Factor of 1691,8005 using Euclid's algorithm

Highest Common Factor of 1691,8005 is 1

Step 1: Since 8005 > 1691, we apply the division lemma to 8005 and 1691, to get

8005 = 1691 x 4 + 1241

Step 2: Since the reminder 1691 ≠ 0, we apply division lemma to 1241 and 1691, to get

1691 = 1241 x 1 + 450

Step 3: We consider the new divisor 1241 and the new remainder 450, and apply the division lemma to get

1241 = 450 x 2 + 341

We consider the new divisor 450 and the new remainder 341,and apply the division lemma to get

450 = 341 x 1 + 109

We consider the new divisor 341 and the new remainder 109,and apply the division lemma to get

341 = 109 x 3 + 14

We consider the new divisor 109 and the new remainder 14,and apply the division lemma to get

109 = 14 x 7 + 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 1691 and 8005 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(11,3) = HCF(14,11) = HCF(109,14) = HCF(341,109) = HCF(450,341) = HCF(1241,450) = HCF(1691,1241) = HCF(8005,1691) .

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Frequently Asked Questions on HCF of 1691, 8005 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 1691, 8005?

Answer: HCF of 1691, 8005 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1691, 8005 using Euclid's Algorithm?

Answer: For arbitrary numbers 1691, 8005 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.