Highest Common Factor of 821, 2254, 6249 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 821, 2254, 6249 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 821, 2254, 6249 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 821, 2254, 6249 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 821, 2254, 6249 is 1.

HCF(821, 2254, 6249) = 1

HCF of 821, 2254, 6249 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 821, 2254, 6249 is 1.

Highest Common Factor of 821,2254,6249 using Euclid's algorithm

Highest Common Factor of 821,2254,6249 is 1

Step 1: Since 2254 > 821, we apply the division lemma to 2254 and 821, to get

2254 = 821 x 2 + 612

Step 2: Since the reminder 821 ≠ 0, we apply division lemma to 612 and 821, to get

821 = 612 x 1 + 209

Step 3: We consider the new divisor 612 and the new remainder 209, and apply the division lemma to get

612 = 209 x 2 + 194

We consider the new divisor 209 and the new remainder 194,and apply the division lemma to get

209 = 194 x 1 + 15

We consider the new divisor 194 and the new remainder 15,and apply the division lemma to get

194 = 15 x 12 + 14

We consider the new divisor 15 and the new remainder 14,and apply the division lemma to get

15 = 14 x 1 + 1

We consider the new divisor 14 and the new remainder 1,and apply the division lemma to get

14 = 1 x 14 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 821 and 2254 is 1

Notice that 1 = HCF(14,1) = HCF(15,14) = HCF(194,15) = HCF(209,194) = HCF(612,209) = HCF(821,612) = HCF(2254,821) .

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

Step 1: Since 6249 > 1, we apply the division lemma to 6249 and 1, to get

6249 = 1 x 6249 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 6249 is 1

Notice that 1 = HCF(6249,1) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 821, 2254, 6249 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 821, 2254, 6249?

Answer: HCF of 821, 2254, 6249 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 821, 2254, 6249 using Euclid's Algorithm?

Answer: For arbitrary numbers 821, 2254, 6249 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.