Highest Common Factor of 696, 385, 68 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 696, 385, 68 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 696, 385, 68 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 696, 385, 68 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 696, 385, 68 is 1.

HCF(696, 385, 68) = 1

HCF of 696, 385, 68 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 696, 385, 68 is 1.

Highest Common Factor of 696,385,68 using Euclid's algorithm

Highest Common Factor of 696,385,68 is 1

Step 1: Since 696 > 385, we apply the division lemma to 696 and 385, to get

696 = 385 x 1 + 311

Step 2: Since the reminder 385 ≠ 0, we apply division lemma to 311 and 385, to get

385 = 311 x 1 + 74

Step 3: We consider the new divisor 311 and the new remainder 74, and apply the division lemma to get

311 = 74 x 4 + 15

We consider the new divisor 74 and the new remainder 15,and apply the division lemma to get

74 = 15 x 4 + 14

We consider the new divisor 15 and the new remainder 14,and apply the division lemma to get

15 = 14 x 1 + 1

We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get

14 = 1 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 696 and 385 is 1

Notice that 1 = HCF(14,1) = HCF(15,14) = HCF(74,15) = HCF(311,74) = HCF(385,311) = HCF(696,385) .

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

Step 1: Since 68 > 1, we apply the division lemma to 68 and 1, to get

68 = 1 x 68 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 68 is 1

Notice that 1 = HCF(68,1) .

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Frequently Asked Questions on HCF of 696, 385, 68 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 696, 385, 68?

Answer: HCF of 696, 385, 68 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 696, 385, 68 using Euclid's Algorithm?

Answer: For arbitrary numbers 696, 385, 68 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.