Highest Common Factor of 96, 563, 185 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 96, 563, 185 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 96, 563, 185 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 96, 563, 185 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 96, 563, 185 is 1.

HCF(96, 563, 185) = 1

HCF of 96, 563, 185 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 96, 563, 185 is 1.

Highest Common Factor of 96,563,185 using Euclid's algorithm

Highest Common Factor of 96,563,185 is 1

Step 1: Since 563 > 96, we apply the division lemma to 563 and 96, to get

563 = 96 x 5 + 83

Step 2: Since the reminder 96 ≠ 0, we apply division lemma to 83 and 96, to get

96 = 83 x 1 + 13

Step 3: We consider the new divisor 83 and the new remainder 13, and apply the division lemma to get

83 = 13 x 6 + 5

We consider the new divisor 13 and the new remainder 5,and apply the division lemma to get

13 = 5 x 2 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 96 and 563 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(13,5) = HCF(83,13) = HCF(96,83) = HCF(563,96) .

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

Step 1: Since 185 > 1, we apply the division lemma to 185 and 1, to get

185 = 1 x 185 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 185 is 1

Notice that 1 = HCF(185,1) .

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Frequently Asked Questions on HCF of 96, 563, 185 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 96, 563, 185?

Answer: HCF of 96, 563, 185 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 96, 563, 185 using Euclid's Algorithm?

Answer: For arbitrary numbers 96, 563, 185 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.