Highest Common Factor of 515, 884, 874 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 515, 884, 874 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 515, 884, 874 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 515, 884, 874 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 515, 884, 874 is 1.

HCF(515, 884, 874) = 1

HCF of 515, 884, 874 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 515, 884, 874 is 1.

Highest Common Factor of 515,884,874 using Euclid's algorithm

Highest Common Factor of 515,884,874 is 1

Step 1: Since 884 > 515, we apply the division lemma to 884 and 515, to get

884 = 515 x 1 + 369

Step 2: Since the reminder 515 ≠ 0, we apply division lemma to 369 and 515, to get

515 = 369 x 1 + 146

Step 3: We consider the new divisor 369 and the new remainder 146, and apply the division lemma to get

369 = 146 x 2 + 77

We consider the new divisor 146 and the new remainder 77,and apply the division lemma to get

146 = 77 x 1 + 69

We consider the new divisor 77 and the new remainder 69,and apply the division lemma to get

77 = 69 x 1 + 8

We consider the new divisor 69 and the new remainder 8,and apply the division lemma to get

69 = 8 x 8 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 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 515 and 884 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(69,8) = HCF(77,69) = HCF(146,77) = HCF(369,146) = HCF(515,369) = HCF(884,515) .

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

Step 1: Since 874 > 1, we apply the division lemma to 874 and 1, to get

874 = 1 x 874 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 874 is 1

Notice that 1 = HCF(874,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 515, 884, 874 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 515, 884, 874?

Answer: HCF of 515, 884, 874 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 515, 884, 874 using Euclid's Algorithm?

Answer: For arbitrary numbers 515, 884, 874 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.