Highest Common Factor of 815, 420, 943, 31 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 815, 420, 943, 31 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 815, 420, 943, 31 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 815, 420, 943, 31 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 815, 420, 943, 31 is 1.

HCF(815, 420, 943, 31) = 1

HCF of 815, 420, 943, 31 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 815, 420, 943, 31 is 1.

Highest Common Factor of 815,420,943,31 using Euclid's algorithm

Highest Common Factor of 815,420,943,31 is 1

Step 1: Since 815 > 420, we apply the division lemma to 815 and 420, to get

815 = 420 x 1 + 395

Step 2: Since the reminder 420 ≠ 0, we apply division lemma to 395 and 420, to get

420 = 395 x 1 + 25

Step 3: We consider the new divisor 395 and the new remainder 25, and apply the division lemma to get

395 = 25 x 15 + 20

We consider the new divisor 25 and the new remainder 20,and apply the division lemma to get

25 = 20 x 1 + 5

We consider the new divisor 20 and the new remainder 5,and apply the division lemma to get

20 = 5 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 5, the HCF of 815 and 420 is 5

Notice that 5 = HCF(20,5) = HCF(25,20) = HCF(395,25) = HCF(420,395) = HCF(815,420) .

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

Step 1: Since 943 > 5, we apply the division lemma to 943 and 5, to get

943 = 5 x 188 + 3

Step 2: Since the reminder 5 ≠ 0, we apply division lemma to 3 and 5, to get

5 = 3 x 1 + 2

Step 3: We consider the new divisor 3 and the new remainder 2, and apply the division lemma to get

3 = 2 x 1 + 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 5 and 943 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(943,5) .

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

Step 1: Since 31 > 1, we apply the division lemma to 31 and 1, to get

31 = 1 x 31 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 31 is 1

Notice that 1 = HCF(31,1) .

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Frequently Asked Questions on HCF of 815, 420, 943, 31 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 815, 420, 943, 31?

Answer: HCF of 815, 420, 943, 31 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 815, 420, 943, 31 using Euclid's Algorithm?

Answer: For arbitrary numbers 815, 420, 943, 31 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.