Highest Common Factor of 800, 8303, 3657 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 800, 8303, 3657 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 800, 8303, 3657 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 800, 8303, 3657 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 800, 8303, 3657 is 1.

HCF(800, 8303, 3657) = 1

HCF of 800, 8303, 3657 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 800, 8303, 3657 is 1.

Highest Common Factor of 800,8303,3657 using Euclid's algorithm

Highest Common Factor of 800,8303,3657 is 1

Step 1: Since 8303 > 800, we apply the division lemma to 8303 and 800, to get

8303 = 800 x 10 + 303

Step 2: Since the reminder 800 ≠ 0, we apply division lemma to 303 and 800, to get

800 = 303 x 2 + 194

Step 3: We consider the new divisor 303 and the new remainder 194, and apply the division lemma to get

303 = 194 x 1 + 109

We consider the new divisor 194 and the new remainder 109,and apply the division lemma to get

194 = 109 x 1 + 85

We consider the new divisor 109 and the new remainder 85,and apply the division lemma to get

109 = 85 x 1 + 24

We consider the new divisor 85 and the new remainder 24,and apply the division lemma to get

85 = 24 x 3 + 13

We consider the new divisor 24 and the new remainder 13,and apply the division lemma to get

24 = 13 x 1 + 11

We consider the new divisor 13 and the new remainder 11,and apply the division lemma to get

13 = 11 x 1 + 2

We consider the new divisor 11 and the new remainder 2,and apply the division lemma to get

11 = 2 x 5 + 1

We consider the new divisor 2 and the new remainder 1,and apply the division lemma to get

2 = 1 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 800 and 8303 is 1

Notice that 1 = HCF(2,1) = HCF(11,2) = HCF(13,11) = HCF(24,13) = HCF(85,24) = HCF(109,85) = HCF(194,109) = HCF(303,194) = HCF(800,303) = HCF(8303,800) .

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

Step 1: Since 3657 > 1, we apply the division lemma to 3657 and 1, to get

3657 = 1 x 3657 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 3657 is 1

Notice that 1 = HCF(3657,1) .

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Frequently Asked Questions on HCF of 800, 8303, 3657 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 800, 8303, 3657?

Answer: HCF of 800, 8303, 3657 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 800, 8303, 3657 using Euclid's Algorithm?

Answer: For arbitrary numbers 800, 8303, 3657 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.