Highest Common Factor of 393, 8116, 2400 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 393, 8116, 2400 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 393, 8116, 2400 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 393, 8116, 2400 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 393, 8116, 2400 is 1.

HCF(393, 8116, 2400) = 1

HCF of 393, 8116, 2400 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 393, 8116, 2400 is 1.

Highest Common Factor of 393,8116,2400 using Euclid's algorithm

Highest Common Factor of 393,8116,2400 is 1

Step 1: Since 8116 > 393, we apply the division lemma to 8116 and 393, to get

8116 = 393 x 20 + 256

Step 2: Since the reminder 393 ≠ 0, we apply division lemma to 256 and 393, to get

393 = 256 x 1 + 137

Step 3: We consider the new divisor 256 and the new remainder 137, and apply the division lemma to get

256 = 137 x 1 + 119

We consider the new divisor 137 and the new remainder 119,and apply the division lemma to get

137 = 119 x 1 + 18

We consider the new divisor 119 and the new remainder 18,and apply the division lemma to get

119 = 18 x 6 + 11

We consider the new divisor 18 and the new remainder 11,and apply the division lemma to get

18 = 11 x 1 + 7

We consider the new divisor 11 and the new remainder 7,and apply the division lemma to get

11 = 7 x 1 + 4

We consider the new divisor 7 and the new remainder 4,and apply the division lemma to get

7 = 4 x 1 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 1

We consider the new divisor 3 and the new remainder 1,and apply the division lemma 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 393 and 8116 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(7,4) = HCF(11,7) = HCF(18,11) = HCF(119,18) = HCF(137,119) = HCF(256,137) = HCF(393,256) = HCF(8116,393) .

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

Step 1: Since 2400 > 1, we apply the division lemma to 2400 and 1, to get

2400 = 1 x 2400 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 2400 is 1

Notice that 1 = HCF(2400,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 393, 8116, 2400 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 393, 8116, 2400?

Answer: HCF of 393, 8116, 2400 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 393, 8116, 2400 using Euclid's Algorithm?

Answer: For arbitrary numbers 393, 8116, 2400 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.