Highest Common Factor of 831, 2241, 1417 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 831, 2241, 1417 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 831, 2241, 1417 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 831, 2241, 1417 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 831, 2241, 1417 is 1.

HCF(831, 2241, 1417) = 1

HCF of 831, 2241, 1417 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 831, 2241, 1417 is 1.

Highest Common Factor of 831,2241,1417 using Euclid's algorithm

Highest Common Factor of 831,2241,1417 is 1

Step 1: Since 2241 > 831, we apply the division lemma to 2241 and 831, to get

2241 = 831 x 2 + 579

Step 2: Since the reminder 831 ≠ 0, we apply division lemma to 579 and 831, to get

831 = 579 x 1 + 252

Step 3: We consider the new divisor 579 and the new remainder 252, and apply the division lemma to get

579 = 252 x 2 + 75

We consider the new divisor 252 and the new remainder 75,and apply the division lemma to get

252 = 75 x 3 + 27

We consider the new divisor 75 and the new remainder 27,and apply the division lemma to get

75 = 27 x 2 + 21

We consider the new divisor 27 and the new remainder 21,and apply the division lemma to get

27 = 21 x 1 + 6

We consider the new divisor 21 and the new remainder 6,and apply the division lemma to get

21 = 6 x 3 + 3

We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get

6 = 3 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 831 and 2241 is 3

Notice that 3 = HCF(6,3) = HCF(21,6) = HCF(27,21) = HCF(75,27) = HCF(252,75) = HCF(579,252) = HCF(831,579) = HCF(2241,831) .

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

Step 1: Since 1417 > 3, we apply the division lemma to 1417 and 3, to get

1417 = 3 x 472 + 1

Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get

3 = 1 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 1417 is 1

Notice that 1 = HCF(3,1) = HCF(1417,3) .

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Frequently Asked Questions on HCF of 831, 2241, 1417 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 831, 2241, 1417?

Answer: HCF of 831, 2241, 1417 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 831, 2241, 1417 using Euclid's Algorithm?

Answer: For arbitrary numbers 831, 2241, 1417 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.