Highest Common Factor of 823, 996, 18 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 823, 996, 18 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 823, 996, 18 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 823, 996, 18 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 823, 996, 18 is 1.

HCF(823, 996, 18) = 1

HCF of 823, 996, 18 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 823, 996, 18 is 1.

Highest Common Factor of 823,996,18 using Euclid's algorithm

Highest Common Factor of 823,996,18 is 1

Step 1: Since 996 > 823, we apply the division lemma to 996 and 823, to get

996 = 823 x 1 + 173

Step 2: Since the reminder 823 ≠ 0, we apply division lemma to 173 and 823, to get

823 = 173 x 4 + 131

Step 3: We consider the new divisor 173 and the new remainder 131, and apply the division lemma to get

173 = 131 x 1 + 42

We consider the new divisor 131 and the new remainder 42,and apply the division lemma to get

131 = 42 x 3 + 5

We consider the new divisor 42 and the new remainder 5,and apply the division lemma to get

42 = 5 x 8 + 2

We consider the new divisor 5 and the new remainder 2,and apply the division lemma to get

5 = 2 x 2 + 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 823 and 996 is 1

Notice that 1 = HCF(2,1) = HCF(5,2) = HCF(42,5) = HCF(131,42) = HCF(173,131) = HCF(823,173) = HCF(996,823) .

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

Step 1: Since 18 > 1, we apply the division lemma to 18 and 1, to get

18 = 1 x 18 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 18 is 1

Notice that 1 = HCF(18,1) .

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Frequently Asked Questions on HCF of 823, 996, 18 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 823, 996, 18?

Answer: HCF of 823, 996, 18 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 823, 996, 18 using Euclid's Algorithm?

Answer: For arbitrary numbers 823, 996, 18 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.