Highest Common Factor of 727, 420, 605 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 727, 420, 605 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 727, 420, 605 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 727, 420, 605 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 727, 420, 605 is 1.

HCF(727, 420, 605) = 1

HCF of 727, 420, 605 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 727, 420, 605 is 1.

Highest Common Factor of 727,420,605 using Euclid's algorithm

Highest Common Factor of 727,420,605 is 1

Step 1: Since 727 > 420, we apply the division lemma to 727 and 420, to get

727 = 420 x 1 + 307

Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 307 and 420, to get

420 = 307 x 1 + 113

Step 3: We consider the new divisor 307 and the new remainder 113, and apply the division lemma to get

307 = 113 x 2 + 81

We consider the new divisor 113 and the new remainder 81,and apply the division lemma to get

113 = 81 x 1 + 32

We consider the new divisor 81 and the new remainder 32,and apply the division lemma to get

81 = 32 x 2 + 17

We consider the new divisor 32 and the new remainder 17,and apply the division lemma to get

32 = 17 x 1 + 15

We consider the new divisor 17 and the new remainder 15,and apply the division lemma to get

17 = 15 x 1 + 2

We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get

15 = 2 x 7 + 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 727 and 420 is 1

Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(17,15) = HCF(32,17) = HCF(81,32) = HCF(113,81) = HCF(307,113) = HCF(420,307) = HCF(727,420) .

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

Step 1: Since 605 > 1, we apply the division lemma to 605 and 1, to get

605 = 1 x 605 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 605 is 1

Notice that 1 = HCF(605,1) .

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Frequently Asked Questions on HCF of 727, 420, 605 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 727, 420, 605?

Answer: HCF of 727, 420, 605 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 727, 420, 605 using Euclid's Algorithm?

Answer: For arbitrary numbers 727, 420, 605 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.