Highest Common Factor of 397, 688, 765 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 397, 688, 765 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 397, 688, 765 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 397, 688, 765 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 397, 688, 765 is 1.

HCF(397, 688, 765) = 1

HCF of 397, 688, 765 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 397, 688, 765 is 1.

Highest Common Factor of 397,688,765 using Euclid's algorithm

Highest Common Factor of 397,688,765 is 1

Step 1: Since 688 > 397, we apply the division lemma to 688 and 397, to get

688 = 397 x 1 + 291

Step 2: Since the reminder 397 ≠ 0, we apply division lemma to 291 and 397, to get

397 = 291 x 1 + 106

Step 3: We consider the new divisor 291 and the new remainder 106, and apply the division lemma to get

291 = 106 x 2 + 79

We consider the new divisor 106 and the new remainder 79,and apply the division lemma to get

106 = 79 x 1 + 27

We consider the new divisor 79 and the new remainder 27,and apply the division lemma to get

79 = 27 x 2 + 25

We consider the new divisor 27 and the new remainder 25,and apply the division lemma to get

27 = 25 x 1 + 2

We consider the new divisor 25 and the new remainder 2,and apply the division lemma to get

25 = 2 x 12 + 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 397 and 688 is 1

Notice that 1 = HCF(2,1) = HCF(25,2) = HCF(27,25) = HCF(79,27) = HCF(106,79) = HCF(291,106) = HCF(397,291) = HCF(688,397) .

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

Step 1: Since 765 > 1, we apply the division lemma to 765 and 1, to get

765 = 1 x 765 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 765 is 1

Notice that 1 = HCF(765,1) .

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Frequently Asked Questions on HCF of 397, 688, 765 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 397, 688, 765?

Answer: HCF of 397, 688, 765 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 397, 688, 765 using Euclid's Algorithm?

Answer: For arbitrary numbers 397, 688, 765 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.