Highest Common Factor of 853, 6284, 2208 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 853, 6284, 2208 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 853, 6284, 2208 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 853, 6284, 2208 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 853, 6284, 2208 is 1.

HCF(853, 6284, 2208) = 1

HCF of 853, 6284, 2208 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 853, 6284, 2208 is 1.

Highest Common Factor of 853,6284,2208 using Euclid's algorithm

Highest Common Factor of 853,6284,2208 is 1

Step 1: Since 6284 > 853, we apply the division lemma to 6284 and 853, to get

6284 = 853 x 7 + 313

Step 2: Since the reminder 853 ≠ 0, we apply division lemma to 313 and 853, to get

853 = 313 x 2 + 227

Step 3: We consider the new divisor 313 and the new remainder 227, and apply the division lemma to get

313 = 227 x 1 + 86

We consider the new divisor 227 and the new remainder 86,and apply the division lemma to get

227 = 86 x 2 + 55

We consider the new divisor 86 and the new remainder 55,and apply the division lemma to get

86 = 55 x 1 + 31

We consider the new divisor 55 and the new remainder 31,and apply the division lemma to get

55 = 31 x 1 + 24

We consider the new divisor 31 and the new remainder 24,and apply the division lemma to get

31 = 24 x 1 + 7

We consider the new divisor 24 and the new remainder 7,and apply the division lemma to get

24 = 7 x 3 + 3

We consider the new divisor 7 and the new remainder 3,and apply the division lemma to get

7 = 3 x 2 + 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 853 and 6284 is 1

Notice that 1 = HCF(3,1) = HCF(7,3) = HCF(24,7) = HCF(31,24) = HCF(55,31) = HCF(86,55) = HCF(227,86) = HCF(313,227) = HCF(853,313) = HCF(6284,853) .

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

Step 1: Since 2208 > 1, we apply the division lemma to 2208 and 1, to get

2208 = 1 x 2208 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 2208 is 1

Notice that 1 = HCF(2208,1) .

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Frequently Asked Questions on HCF of 853, 6284, 2208 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 853, 6284, 2208?

Answer: HCF of 853, 6284, 2208 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 853, 6284, 2208 using Euclid's Algorithm?

Answer: For arbitrary numbers 853, 6284, 2208 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.