Highest Common Factor of 397, 560, 735 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, 560, 735 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 397, 560, 735 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, 560, 735 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, 560, 735 is 1.

HCF(397, 560, 735) = 1

HCF of 397, 560, 735 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, 560, 735 is 1.

Highest Common Factor of 397,560,735 using Euclid's algorithm

Highest Common Factor of 397,560,735 is 1

Step 1: Since 560 > 397, we apply the division lemma to 560 and 397, to get

560 = 397 x 1 + 163

Step 2: Since the reminder 397 ≠ 0, we apply division lemma to 163 and 397, to get

397 = 163 x 2 + 71

Step 3: We consider the new divisor 163 and the new remainder 71, and apply the division lemma to get

163 = 71 x 2 + 21

We consider the new divisor 71 and the new remainder 21,and apply the division lemma to get

71 = 21 x 3 + 8

We consider the new divisor 21 and the new remainder 8,and apply the division lemma to get

21 = 8 x 2 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

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

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 560 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(21,8) = HCF(71,21) = HCF(163,71) = HCF(397,163) = HCF(560,397) .

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

Step 1: Since 735 > 1, we apply the division lemma to 735 and 1, to get

735 = 1 x 735 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 735 is 1

Notice that 1 = HCF(735,1) .

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Frequently Asked Questions on HCF of 397, 560, 735 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, 560, 735?

Answer: HCF of 397, 560, 735 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 397, 560, 735 using Euclid's Algorithm?

Answer: For arbitrary numbers 397, 560, 735 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.