Highest Common Factor of 691, 20469 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 691, 20469 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 691, 20469 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 691, 20469 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 691, 20469 is 1.

HCF(691, 20469) = 1

HCF of 691, 20469 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 691, 20469 is 1.

Highest Common Factor of 691,20469 using Euclid's algorithm

Highest Common Factor of 691,20469 is 1

Step 1: Since 20469 > 691, we apply the division lemma to 20469 and 691, to get

20469 = 691 x 29 + 430

Step 2: Since the reminder 691 ≠ 0, we apply division lemma to 430 and 691, to get

691 = 430 x 1 + 261

Step 3: We consider the new divisor 430 and the new remainder 261, and apply the division lemma to get

430 = 261 x 1 + 169

We consider the new divisor 261 and the new remainder 169,and apply the division lemma to get

261 = 169 x 1 + 92

We consider the new divisor 169 and the new remainder 92,and apply the division lemma to get

169 = 92 x 1 + 77

We consider the new divisor 92 and the new remainder 77,and apply the division lemma to get

92 = 77 x 1 + 15

We consider the new divisor 77 and the new remainder 15,and apply the division lemma to get

77 = 15 x 5 + 2

We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get

15 = 2 x 7 + 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 691 and 20469 is 1

Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(77,15) = HCF(92,77) = HCF(169,92) = HCF(261,169) = HCF(430,261) = HCF(691,430) = HCF(20469,691) .

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Frequently Asked Questions on HCF of 691, 20469 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 691, 20469?

Answer: HCF of 691, 20469 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 691, 20469 using Euclid's Algorithm?

Answer: For arbitrary numbers 691, 20469 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.