Highest Common Factor of 819, 310, 653 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 819, 310, 653 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 819, 310, 653 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 819, 310, 653 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 819, 310, 653 is 1.

HCF(819, 310, 653) = 1

HCF of 819, 310, 653 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 819, 310, 653 is 1.

Highest Common Factor of 819,310,653 using Euclid's algorithm

Highest Common Factor of 819,310,653 is 1

Step 1: Since 819 > 310, we apply the division lemma to 819 and 310, to get

819 = 310 x 2 + 199

Step 2: Since the reminder 310 ≠ 0, we apply division lemma to 199 and 310, to get

310 = 199 x 1 + 111

Step 3: We consider the new divisor 199 and the new remainder 111, and apply the division lemma to get

199 = 111 x 1 + 88

We consider the new divisor 111 and the new remainder 88,and apply the division lemma to get

111 = 88 x 1 + 23

We consider the new divisor 88 and the new remainder 23,and apply the division lemma to get

88 = 23 x 3 + 19

We consider the new divisor 23 and the new remainder 19,and apply the division lemma to get

23 = 19 x 1 + 4

We consider the new divisor 19 and the new remainder 4,and apply the division lemma to get

19 = 4 x 4 + 3

We consider the new divisor 4 and the new remainder 3,and apply the division lemma to get

4 = 3 x 1 + 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 819 and 310 is 1

Notice that 1 = HCF(3,1) = HCF(4,3) = HCF(19,4) = HCF(23,19) = HCF(88,23) = HCF(111,88) = HCF(199,111) = HCF(310,199) = HCF(819,310) .

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

Step 1: Since 653 > 1, we apply the division lemma to 653 and 1, to get

653 = 1 x 653 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 653 is 1

Notice that 1 = HCF(653,1) .

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Frequently Asked Questions on HCF of 819, 310, 653 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 819, 310, 653?

Answer: HCF of 819, 310, 653 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 819, 310, 653 using Euclid's Algorithm?

Answer: For arbitrary numbers 819, 310, 653 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.