Highest Common Factor of 854, 289, 412 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 854, 289, 412 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 854, 289, 412 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 854, 289, 412 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 854, 289, 412 is 1.

HCF(854, 289, 412) = 1

HCF of 854, 289, 412 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 854, 289, 412 is 1.

Highest Common Factor of 854,289,412 using Euclid's algorithm

Highest Common Factor of 854,289,412 is 1

Step 1: Since 854 > 289, we apply the division lemma to 854 and 289, to get

854 = 289 x 2 + 276

Step 2: Since the reminder 289 ≠ 0, we apply division lemma to 276 and 289, to get

289 = 276 x 1 + 13

Step 3: We consider the new divisor 276 and the new remainder 13, and apply the division lemma to get

276 = 13 x 21 + 3

We consider the new divisor 13 and the new remainder 3,and apply the division lemma to get

13 = 3 x 4 + 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 854 and 289 is 1

Notice that 1 = HCF(3,1) = HCF(13,3) = HCF(276,13) = HCF(289,276) = HCF(854,289) .

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

Step 1: Since 412 > 1, we apply the division lemma to 412 and 1, to get

412 = 1 x 412 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 412 is 1

Notice that 1 = HCF(412,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 854, 289, 412 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 854, 289, 412?

Answer: HCF of 854, 289, 412 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 854, 289, 412 using Euclid's Algorithm?

Answer: For arbitrary numbers 854, 289, 412 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.