Highest Common Factor of 421, 729, 386 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 421, 729, 386 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 421, 729, 386 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 421, 729, 386 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 421, 729, 386 is 1.

HCF(421, 729, 386) = 1

HCF of 421, 729, 386 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 421, 729, 386 is 1.

Highest Common Factor of 421,729,386 using Euclid's algorithm

Highest Common Factor of 421,729,386 is 1

Step 1: Since 729 > 421, we apply the division lemma to 729 and 421, to get

729 = 421 x 1 + 308

Step 2: Since the reminder 421 ≠ 0, we apply division lemma to 308 and 421, to get

421 = 308 x 1 + 113

Step 3: We consider the new divisor 308 and the new remainder 113, and apply the division lemma to get

308 = 113 x 2 + 82

We consider the new divisor 113 and the new remainder 82,and apply the division lemma to get

113 = 82 x 1 + 31

We consider the new divisor 82 and the new remainder 31,and apply the division lemma to get

82 = 31 x 2 + 20

We consider the new divisor 31 and the new remainder 20,and apply the division lemma to get

31 = 20 x 1 + 11

We consider the new divisor 20 and the new remainder 11,and apply the division lemma to get

20 = 11 x 1 + 9

We consider the new divisor 11 and the new remainder 9,and apply the division lemma to get

11 = 9 x 1 + 2

We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get

9 = 2 x 4 + 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 421 and 729 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(11,9) = HCF(20,11) = HCF(31,20) = HCF(82,31) = HCF(113,82) = HCF(308,113) = HCF(421,308) = HCF(729,421) .

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

Step 1: Since 386 > 1, we apply the division lemma to 386 and 1, to get

386 = 1 x 386 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 386 is 1

Notice that 1 = HCF(386,1) .

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Frequently Asked Questions on HCF of 421, 729, 386 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 421, 729, 386?

Answer: HCF of 421, 729, 386 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 421, 729, 386 using Euclid's Algorithm?

Answer: For arbitrary numbers 421, 729, 386 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.