Highest Common Factor of 421, 381, 731 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, 381, 731 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 421, 381, 731 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, 381, 731 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, 381, 731 is 1.

HCF(421, 381, 731) = 1

HCF of 421, 381, 731 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, 381, 731 is 1.

Highest Common Factor of 421,381,731 using Euclid's algorithm

Highest Common Factor of 421,381,731 is 1

Step 1: Since 421 > 381, we apply the division lemma to 421 and 381, to get

421 = 381 x 1 + 40

Step 2: Since the reminder 381 ≠ 0, we apply division lemma to 40 and 381, to get

381 = 40 x 9 + 21

Step 3: We consider the new divisor 40 and the new remainder 21, and apply the division lemma to get

40 = 21 x 1 + 19

We consider the new divisor 21 and the new remainder 19,and apply the division lemma to get

21 = 19 x 1 + 2

We consider the new divisor 19 and the new remainder 2,and apply the division lemma to get

19 = 2 x 9 + 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 381 is 1

Notice that 1 = HCF(2,1) = HCF(19,2) = HCF(21,19) = HCF(40,21) = HCF(381,40) = HCF(421,381) .

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

Step 1: Since 731 > 1, we apply the division lemma to 731 and 1, to get

731 = 1 x 731 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 731 is 1

Notice that 1 = HCF(731,1) .

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Frequently Asked Questions on HCF of 421, 381, 731 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, 381, 731?

Answer: HCF of 421, 381, 731 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 421, 381, 731 using Euclid's Algorithm?

Answer: For arbitrary numbers 421, 381, 731 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.