Highest Common Factor of 864, 232, 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 864, 232, 697 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 864, 232, 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 864, 232, 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 864, 232, 697 is 1.

HCF(864, 232, 697) = 1

HCF of 864, 232, 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 864, 232, 697 is 1.

Highest Common Factor of 864,232,697 using Euclid's algorithm

Highest Common Factor of 864,232,697 is 1

Step 1: Since 864 > 232, we apply the division lemma to 864 and 232, to get

864 = 232 x 3 + 168

Step 2: Since the reminder 232 ≠ 0, we apply division lemma to 168 and 232, to get

232 = 168 x 1 + 64

Step 3: We consider the new divisor 168 and the new remainder 64, and apply the division lemma to get

168 = 64 x 2 + 40

We consider the new divisor 64 and the new remainder 40,and apply the division lemma to get

64 = 40 x 1 + 24

We consider the new divisor 40 and the new remainder 24,and apply the division lemma to get

40 = 24 x 1 + 16

We consider the new divisor 24 and the new remainder 16,and apply the division lemma to get

24 = 16 x 1 + 8

We consider the new divisor 16 and the new remainder 8,and apply the division lemma to get

16 = 8 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 8, the HCF of 864 and 232 is 8

Notice that 8 = HCF(16,8) = HCF(24,16) = HCF(40,24) = HCF(64,40) = HCF(168,64) = HCF(232,168) = HCF(864,232) .

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

Step 1: Since 697 > 8, we apply the division lemma to 697 and 8, to get

697 = 8 x 87 + 1

Step 2: Since the reminder 8 ≠ 0, we apply division lemma to 1 and 8, to get

8 = 1 x 8 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 8 and 697 is 1

Notice that 1 = HCF(8,1) = HCF(697,8) .

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Frequently Asked Questions on HCF of 864, 232, 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 864, 232, 697?

Answer: HCF of 864, 232, 697 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 864, 232, 697 using Euclid's Algorithm?

Answer: For arbitrary numbers 864, 232, 697 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.