Highest Common Factor of 8314, 3485, 73694 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 8314, 3485, 73694 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8314, 3485, 73694 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 8314, 3485, 73694 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 8314, 3485, 73694 is 1.

HCF(8314, 3485, 73694) = 1

HCF of 8314, 3485, 73694 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 8314, 3485, 73694 is 1.

Highest Common Factor of 8314,3485,73694 using Euclid's algorithm

Highest Common Factor of 8314,3485,73694 is 1

Step 1: Since 8314 > 3485, we apply the division lemma to 8314 and 3485, to get

8314 = 3485 x 2 + 1344

Step 2: Since the reminder 3485 ≠ 0, we apply division lemma to 1344 and 3485, to get

3485 = 1344 x 2 + 797

Step 3: We consider the new divisor 1344 and the new remainder 797, and apply the division lemma to get

1344 = 797 x 1 + 547

We consider the new divisor 797 and the new remainder 547,and apply the division lemma to get

797 = 547 x 1 + 250

We consider the new divisor 547 and the new remainder 250,and apply the division lemma to get

547 = 250 x 2 + 47

We consider the new divisor 250 and the new remainder 47,and apply the division lemma to get

250 = 47 x 5 + 15

We consider the new divisor 47 and the new remainder 15,and apply the division lemma to get

47 = 15 x 3 + 2

We consider the new divisor 15 and the new remainder 2,and apply the division lemma to get

15 = 2 x 7 + 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 8314 and 3485 is 1

Notice that 1 = HCF(2,1) = HCF(15,2) = HCF(47,15) = HCF(250,47) = HCF(547,250) = HCF(797,547) = HCF(1344,797) = HCF(3485,1344) = HCF(8314,3485) .

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

Step 1: Since 73694 > 1, we apply the division lemma to 73694 and 1, to get

73694 = 1 x 73694 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 73694 is 1

Notice that 1 = HCF(73694,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 8314, 3485, 73694 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 8314, 3485, 73694?

Answer: HCF of 8314, 3485, 73694 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8314, 3485, 73694 using Euclid's Algorithm?

Answer: For arbitrary numbers 8314, 3485, 73694 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.