Highest Common Factor of 1354, 1817, 84191 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 1354, 1817, 84191 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1354, 1817, 84191 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 1354, 1817, 84191 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 1354, 1817, 84191 is 1.

HCF(1354, 1817, 84191) = 1

HCF of 1354, 1817, 84191 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 1354, 1817, 84191 is 1.

Highest Common Factor of 1354,1817,84191 using Euclid's algorithm

Highest Common Factor of 1354,1817,84191 is 1

Step 1: Since 1817 > 1354, we apply the division lemma to 1817 and 1354, to get

1817 = 1354 x 1 + 463

Step 2: Since the reminder 1354 ≠ 0, we apply division lemma to 463 and 1354, to get

1354 = 463 x 2 + 428

Step 3: We consider the new divisor 463 and the new remainder 428, and apply the division lemma to get

463 = 428 x 1 + 35

We consider the new divisor 428 and the new remainder 35,and apply the division lemma to get

428 = 35 x 12 + 8

We consider the new divisor 35 and the new remainder 8,and apply the division lemma to get

35 = 8 x 4 + 3

We consider the new divisor 8 and the new remainder 3,and apply the division lemma to get

8 = 3 x 2 + 2

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 1354 and 1817 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(8,3) = HCF(35,8) = HCF(428,35) = HCF(463,428) = HCF(1354,463) = HCF(1817,1354) .

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

Step 1: Since 84191 > 1, we apply the division lemma to 84191 and 1, to get

84191 = 1 x 84191 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 84191 is 1

Notice that 1 = HCF(84191,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 1354, 1817, 84191 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 1354, 1817, 84191?

Answer: HCF of 1354, 1817, 84191 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1354, 1817, 84191 using Euclid's Algorithm?

Answer: For arbitrary numbers 1354, 1817, 84191 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.