Highest Common Factor of 730, 409, 617 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 730, 409, 617 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 730, 409, 617 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 730, 409, 617 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 730, 409, 617 is 1.

HCF(730, 409, 617) = 1

HCF of 730, 409, 617 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 730, 409, 617 is 1.

Highest Common Factor of 730,409,617 using Euclid's algorithm

Highest Common Factor of 730,409,617 is 1

Step 1: Since 730 > 409, we apply the division lemma to 730 and 409, to get

730 = 409 x 1 + 321

Step 2: Since the reminder 409 ≠ 0, we apply division lemma to 321 and 409, to get

409 = 321 x 1 + 88

Step 3: We consider the new divisor 321 and the new remainder 88, and apply the division lemma to get

321 = 88 x 3 + 57

We consider the new divisor 88 and the new remainder 57,and apply the division lemma to get

88 = 57 x 1 + 31

We consider the new divisor 57 and the new remainder 31,and apply the division lemma to get

57 = 31 x 1 + 26

We consider the new divisor 31 and the new remainder 26,and apply the division lemma to get

31 = 26 x 1 + 5

We consider the new divisor 26 and the new remainder 5,and apply the division lemma to get

26 = 5 x 5 + 1

We consider the new divisor 5 and the new remainder 1,and apply the division lemma to get

5 = 1 x 5 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 730 and 409 is 1

Notice that 1 = HCF(5,1) = HCF(26,5) = HCF(31,26) = HCF(57,31) = HCF(88,57) = HCF(321,88) = HCF(409,321) = HCF(730,409) .

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

Step 1: Since 617 > 1, we apply the division lemma to 617 and 1, to get

617 = 1 x 617 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 617 is 1

Notice that 1 = HCF(617,1) .

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Frequently Asked Questions on HCF of 730, 409, 617 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 730, 409, 617?

Answer: HCF of 730, 409, 617 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 730, 409, 617 using Euclid's Algorithm?

Answer: For arbitrary numbers 730, 409, 617 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.