Highest Common Factor of 397, 506, 340 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, 506, 340 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 397, 506, 340 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, 506, 340 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, 506, 340 is 1.

HCF(397, 506, 340) = 1

HCF of 397, 506, 340 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, 506, 340 is 1.

Highest Common Factor of 397,506,340 using Euclid's algorithm

Highest Common Factor of 397,506,340 is 1

Step 1: Since 506 > 397, we apply the division lemma to 506 and 397, to get

506 = 397 x 1 + 109

Step 2: Since the reminder 397 ≠ 0, we apply division lemma to 109 and 397, to get

397 = 109 x 3 + 70

Step 3: We consider the new divisor 109 and the new remainder 70, and apply the division lemma to get

109 = 70 x 1 + 39

We consider the new divisor 70 and the new remainder 39,and apply the division lemma to get

70 = 39 x 1 + 31

We consider the new divisor 39 and the new remainder 31,and apply the division lemma to get

39 = 31 x 1 + 8

We consider the new divisor 31 and the new remainder 8,and apply the division lemma to get

31 = 8 x 3 + 7

We consider the new divisor 8 and the new remainder 7,and apply the division lemma to get

8 = 7 x 1 + 1

We consider the new divisor 7 and the new remainder 1,and apply the division lemma to get

7 = 1 x 7 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 397 and 506 is 1

Notice that 1 = HCF(7,1) = HCF(8,7) = HCF(31,8) = HCF(39,31) = HCF(70,39) = HCF(109,70) = HCF(397,109) = HCF(506,397) .

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

Step 1: Since 340 > 1, we apply the division lemma to 340 and 1, to get

340 = 1 x 340 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 340 is 1

Notice that 1 = HCF(340,1) .

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Frequently Asked Questions on HCF of 397, 506, 340 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, 506, 340?

Answer: HCF of 397, 506, 340 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 397, 506, 340 using Euclid's Algorithm?

Answer: For arbitrary numbers 397, 506, 340 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.