Highest Common Factor of 518, 821, 154 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 518, 821, 154 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 518, 821, 154 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 518, 821, 154 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 518, 821, 154 is 1.

HCF(518, 821, 154) = 1

HCF of 518, 821, 154 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 518, 821, 154 is 1.

Highest Common Factor of 518,821,154 using Euclid's algorithm

Highest Common Factor of 518,821,154 is 1

Step 1: Since 821 > 518, we apply the division lemma to 821 and 518, to get

821 = 518 x 1 + 303

Step 2: Since the reminder 518 ≠ 0, we apply division lemma to 303 and 518, to get

518 = 303 x 1 + 215

Step 3: We consider the new divisor 303 and the new remainder 215, and apply the division lemma to get

303 = 215 x 1 + 88

We consider the new divisor 215 and the new remainder 88,and apply the division lemma to get

215 = 88 x 2 + 39

We consider the new divisor 88 and the new remainder 39,and apply the division lemma to get

88 = 39 x 2 + 10

We consider the new divisor 39 and the new remainder 10,and apply the division lemma to get

39 = 10 x 3 + 9

We consider the new divisor 10 and the new remainder 9,and apply the division lemma to get

10 = 9 x 1 + 1

We consider the new divisor 9 and the new remainder 1,and apply the division lemma to get

9 = 1 x 9 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 518 and 821 is 1

Notice that 1 = HCF(9,1) = HCF(10,9) = HCF(39,10) = HCF(88,39) = HCF(215,88) = HCF(303,215) = HCF(518,303) = HCF(821,518) .

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

Step 1: Since 154 > 1, we apply the division lemma to 154 and 1, to get

154 = 1 x 154 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 154 is 1

Notice that 1 = HCF(154,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 518, 821, 154 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 518, 821, 154?

Answer: HCF of 518, 821, 154 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 518, 821, 154 using Euclid's Algorithm?

Answer: For arbitrary numbers 518, 821, 154 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.