Highest Common Factor of 96, 696, 235 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, 696, 235 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 96, 696, 235 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, 696, 235 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, 696, 235 is 1.

HCF(96, 696, 235) = 1

HCF of 96, 696, 235 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, 696, 235 is 1.

Highest Common Factor of 96,696,235 using Euclid's algorithm

Highest Common Factor of 96,696,235 is 1

Step 1: Since 696 > 96, we apply the division lemma to 696 and 96, to get

696 = 96 x 7 + 24

Step 2: Since the reminder 96 ≠ 0, we apply division lemma to 24 and 96, to get

96 = 24 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 24, the HCF of 96 and 696 is 24

Notice that 24 = HCF(96,24) = HCF(696,96) .

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

Step 1: Since 235 > 24, we apply the division lemma to 235 and 24, to get

235 = 24 x 9 + 19

Step 2: Since the reminder 24 ≠ 0, we apply division lemma to 19 and 24, to get

24 = 19 x 1 + 5

Step 3: We consider the new divisor 19 and the new remainder 5, and apply the division lemma to get

19 = 5 x 3 + 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 24 and 235 is 1

Notice that 1 = HCF(4,1) = HCF(5,4) = HCF(19,5) = HCF(24,19) = HCF(235,24) .

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Frequently Asked Questions on HCF of 96, 696, 235 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, 696, 235?

Answer: HCF of 96, 696, 235 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 96, 696, 235 using Euclid's Algorithm?

Answer: For arbitrary numbers 96, 696, 235 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.