Highest Common Factor of 8692, 823 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 8692, 823 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8692, 823 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 8692, 823 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 8692, 823 is 1.

HCF(8692, 823) = 1

HCF of 8692, 823 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 8692, 823 is 1.

Highest Common Factor of 8692,823 using Euclid's algorithm

Highest Common Factor of 8692,823 is 1

Step 1: Since 8692 > 823, we apply the division lemma to 8692 and 823, to get

8692 = 823 x 10 + 462

Step 2: Since the reminder 823 ≠ 0, we apply division lemma to 462 and 823, to get

823 = 462 x 1 + 361

Step 3: We consider the new divisor 462 and the new remainder 361, and apply the division lemma to get

462 = 361 x 1 + 101

We consider the new divisor 361 and the new remainder 101,and apply the division lemma to get

361 = 101 x 3 + 58

We consider the new divisor 101 and the new remainder 58,and apply the division lemma to get

101 = 58 x 1 + 43

We consider the new divisor 58 and the new remainder 43,and apply the division lemma to get

58 = 43 x 1 + 15

We consider the new divisor 43 and the new remainder 15,and apply the division lemma to get

43 = 15 x 2 + 13

We consider the new divisor 15 and the new remainder 13,and apply the division lemma to get

15 = 13 x 1 + 2

We consider the new divisor 13 and the new remainder 2,and apply the division lemma to get

13 = 2 x 6 + 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 8692 and 823 is 1

Notice that 1 = HCF(2,1) = HCF(13,2) = HCF(15,13) = HCF(43,15) = HCF(58,43) = HCF(101,58) = HCF(361,101) = HCF(462,361) = HCF(823,462) = HCF(8692,823) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 8692, 823 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 8692, 823?

Answer: HCF of 8692, 823 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8692, 823 using Euclid's Algorithm?

Answer: For arbitrary numbers 8692, 823 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.