Highest Common Factor of 696, 969, 697 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, 969, 697 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 696, 969, 697 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, 969, 697 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, 969, 697 is 1.

HCF(696, 969, 697) = 1

HCF of 696, 969, 697 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, 969, 697 is 1.

Highest Common Factor of 696,969,697 using Euclid's algorithm

Highest Common Factor of 696,969,697 is 1

Step 1: Since 969 > 696, we apply the division lemma to 969 and 696, to get

969 = 696 x 1 + 273

Step 2: Since the reminder 696 ≠ 0, we apply division lemma to 273 and 696, to get

696 = 273 x 2 + 150

Step 3: We consider the new divisor 273 and the new remainder 150, and apply the division lemma to get

273 = 150 x 1 + 123

We consider the new divisor 150 and the new remainder 123,and apply the division lemma to get

150 = 123 x 1 + 27

We consider the new divisor 123 and the new remainder 27,and apply the division lemma to get

123 = 27 x 4 + 15

We consider the new divisor 27 and the new remainder 15,and apply the division lemma to get

27 = 15 x 1 + 12

We consider the new divisor 15 and the new remainder 12,and apply the division lemma to get

15 = 12 x 1 + 3

We consider the new divisor 12 and the new remainder 3,and apply the division lemma to get

12 = 3 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 696 and 969 is 3

Notice that 3 = HCF(12,3) = HCF(15,12) = HCF(27,15) = HCF(123,27) = HCF(150,123) = HCF(273,150) = HCF(696,273) = HCF(969,696) .

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

Step 1: Since 697 > 3, we apply the division lemma to 697 and 3, to get

697 = 3 x 232 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 697 is 1

Notice that 1 = HCF(3,1) = HCF(697,3) .

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Frequently Asked Questions on HCF of 696, 969, 697 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, 969, 697?

Answer: HCF of 696, 969, 697 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 696, 969, 697 using Euclid's Algorithm?

Answer: For arbitrary numbers 696, 969, 697 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.