Highest Common Factor of 916, 643, 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 916, 643, 823 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 916, 643, 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 916, 643, 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 916, 643, 823 is 1.

HCF(916, 643, 823) = 1

HCF of 916, 643, 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 916, 643, 823 is 1.

Highest Common Factor of 916,643,823 using Euclid's algorithm

Highest Common Factor of 916,643,823 is 1

Step 1: Since 916 > 643, we apply the division lemma to 916 and 643, to get

916 = 643 x 1 + 273

Step 2: Since the reminder 643 ≠ 0, we apply division lemma to 273 and 643, to get

643 = 273 x 2 + 97

Step 3: We consider the new divisor 273 and the new remainder 97, and apply the division lemma to get

273 = 97 x 2 + 79

We consider the new divisor 97 and the new remainder 79,and apply the division lemma to get

97 = 79 x 1 + 18

We consider the new divisor 79 and the new remainder 18,and apply the division lemma to get

79 = 18 x 4 + 7

We consider the new divisor 18 and the new remainder 7,and apply the division lemma to get

18 = 7 x 2 + 4

We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get

7 = 4 x 1 + 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 916 and 643 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(18,7) = HCF(79,18) = HCF(97,79) = HCF(273,97) = HCF(643,273) = HCF(916,643) .

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

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

823 = 1 x 823 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 823 is 1

Notice that 1 = HCF(823,1) .

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Frequently Asked Questions on HCF of 916, 643, 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 916, 643, 823?

Answer: HCF of 916, 643, 823 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 916, 643, 823 using Euclid's Algorithm?

Answer: For arbitrary numbers 916, 643, 823 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.