Highest Common Factor of 431, 618, 721 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 431, 618, 721 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 431, 618, 721 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 431, 618, 721 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 431, 618, 721 is 1.

HCF(431, 618, 721) = 1

HCF of 431, 618, 721 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 431, 618, 721 is 1.

Highest Common Factor of 431,618,721 using Euclid's algorithm

Highest Common Factor of 431,618,721 is 1

Step 1: Since 618 > 431, we apply the division lemma to 618 and 431, to get

618 = 431 x 1 + 187

Step 2: Since the reminder 431 ≠ 0, we apply division lemma to 187 and 431, to get

431 = 187 x 2 + 57

Step 3: We consider the new divisor 187 and the new remainder 57, and apply the division lemma to get

187 = 57 x 3 + 16

We consider the new divisor 57 and the new remainder 16,and apply the division lemma to get

57 = 16 x 3 + 9

We consider the new divisor 16 and the new remainder 9,and apply the division lemma to get

16 = 9 x 1 + 7

We consider the new divisor 9 and the new remainder 7,and apply the division lemma to get

9 = 7 x 1 + 2

We consider the new divisor 7 and the new remainder 2,and apply the division lemma to get

7 = 2 x 3 + 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 431 and 618 is 1

Notice that 1 = HCF(2,1) = HCF(7,2) = HCF(9,7) = HCF(16,9) = HCF(57,16) = HCF(187,57) = HCF(431,187) = HCF(618,431) .

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

Step 1: Since 721 > 1, we apply the division lemma to 721 and 1, to get

721 = 1 x 721 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 721 is 1

Notice that 1 = HCF(721,1) .

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Frequently Asked Questions on HCF of 431, 618, 721 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 431, 618, 721?

Answer: HCF of 431, 618, 721 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 431, 618, 721 using Euclid's Algorithm?

Answer: For arbitrary numbers 431, 618, 721 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.