Highest Common Factor of 923, 663, 696 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 923, 663, 696 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 923, 663, 696 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 923, 663, 696 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 923, 663, 696 is 1.

HCF(923, 663, 696) = 1

HCF of 923, 663, 696 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 923, 663, 696 is 1.

Highest Common Factor of 923,663,696 using Euclid's algorithm

Highest Common Factor of 923,663,696 is 1

Step 1: Since 923 > 663, we apply the division lemma to 923 and 663, to get

923 = 663 x 1 + 260

Step 2: Since the reminder 663 ≠ 0, we apply division lemma to 260 and 663, to get

663 = 260 x 2 + 143

Step 3: We consider the new divisor 260 and the new remainder 143, and apply the division lemma to get

260 = 143 x 1 + 117

We consider the new divisor 143 and the new remainder 117,and apply the division lemma to get

143 = 117 x 1 + 26

We consider the new divisor 117 and the new remainder 26,and apply the division lemma to get

117 = 26 x 4 + 13

We consider the new divisor 26 and the new remainder 13,and apply the division lemma to get

26 = 13 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 13, the HCF of 923 and 663 is 13

Notice that 13 = HCF(26,13) = HCF(117,26) = HCF(143,117) = HCF(260,143) = HCF(663,260) = HCF(923,663) .

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

Step 1: Since 696 > 13, we apply the division lemma to 696 and 13, to get

696 = 13 x 53 + 7

Step 2: Since the reminder 13 ≠ 0, we apply division lemma to 7 and 13, to get

13 = 7 x 1 + 6

Step 3: We consider the new divisor 7 and the new remainder 6, and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1, and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 13 and 696 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(696,13) .

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Frequently Asked Questions on HCF of 923, 663, 696 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 923, 663, 696?

Answer: HCF of 923, 663, 696 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 923, 663, 696 using Euclid's Algorithm?

Answer: For arbitrary numbers 923, 663, 696 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.