Highest Common Factor of 855, 523, 96 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 855, 523, 96 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 855, 523, 96 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 855, 523, 96 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 855, 523, 96 is 1.

HCF(855, 523, 96) = 1

HCF of 855, 523, 96 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 855, 523, 96 is 1.

Highest Common Factor of 855,523,96 using Euclid's algorithm

Highest Common Factor of 855,523,96 is 1

Step 1: Since 855 > 523, we apply the division lemma to 855 and 523, to get

855 = 523 x 1 + 332

Step 2: Since the reminder 523 ≠ 0, we apply division lemma to 332 and 523, to get

523 = 332 x 1 + 191

Step 3: We consider the new divisor 332 and the new remainder 191, and apply the division lemma to get

332 = 191 x 1 + 141

We consider the new divisor 191 and the new remainder 141,and apply the division lemma to get

191 = 141 x 1 + 50

We consider the new divisor 141 and the new remainder 50,and apply the division lemma to get

141 = 50 x 2 + 41

We consider the new divisor 50 and the new remainder 41,and apply the division lemma to get

50 = 41 x 1 + 9

We consider the new divisor 41 and the new remainder 9,and apply the division lemma to get

41 = 9 x 4 + 5

We consider the new divisor 9 and the new remainder 5,and apply the division lemma to get

9 = 5 x 1 + 4

We consider the new divisor 5 and the new remainder 4,and apply the division lemma to get

5 = 4 x 1 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 855 and 523 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(9,5) = HCF(41,9) = HCF(50,41) = HCF(141,50) = HCF(191,141) = HCF(332,191) = HCF(523,332) = HCF(855,523) .

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

Step 1: Since 96 > 1, we apply the division lemma to 96 and 1, to get

96 = 1 x 96 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 96 is 1

Notice that 1 = HCF(96,1) .

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Frequently Asked Questions on HCF of 855, 523, 96 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 855, 523, 96?

Answer: HCF of 855, 523, 96 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 855, 523, 96 using Euclid's Algorithm?

Answer: For arbitrary numbers 855, 523, 96 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.