Highest Common Factor of 854, 3221 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, 3221 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 854, 3221 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, 3221 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, 3221 is 1.

HCF(854, 3221) = 1

HCF of 854, 3221 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, 3221 is 1.

Highest Common Factor of 854,3221 using Euclid's algorithm

Highest Common Factor of 854,3221 is 1

Step 1: Since 3221 > 854, we apply the division lemma to 3221 and 854, to get

3221 = 854 x 3 + 659

Step 2: Since the reminder 854 ≠ 0, we apply division lemma to 659 and 854, to get

854 = 659 x 1 + 195

Step 3: We consider the new divisor 659 and the new remainder 195, and apply the division lemma to get

659 = 195 x 3 + 74

We consider the new divisor 195 and the new remainder 74,and apply the division lemma to get

195 = 74 x 2 + 47

We consider the new divisor 74 and the new remainder 47,and apply the division lemma to get

74 = 47 x 1 + 27

We consider the new divisor 47 and the new remainder 27,and apply the division lemma to get

47 = 27 x 1 + 20

We consider the new divisor 27 and the new remainder 20,and apply the division lemma to get

27 = 20 x 1 + 7

We consider the new divisor 20 and the new remainder 7,and apply the division lemma to get

20 = 7 x 2 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 854 and 3221 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(20,7) = HCF(27,20) = HCF(47,27) = HCF(74,47) = HCF(195,74) = HCF(659,195) = HCF(854,659) = HCF(3221,854) .

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, 3221 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, 3221?

Answer: HCF of 854, 3221 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 854, 3221 using Euclid's Algorithm?

Answer: For arbitrary numbers 854, 3221 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.