Highest Common Factor of 8218, 5646, 74303 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 8218, 5646, 74303 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 8218, 5646, 74303 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 8218, 5646, 74303 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 8218, 5646, 74303 is 1.

HCF(8218, 5646, 74303) = 1

HCF of 8218, 5646, 74303 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 8218, 5646, 74303 is 1.

Highest Common Factor of 8218,5646,74303 using Euclid's algorithm

Highest Common Factor of 8218,5646,74303 is 1

Step 1: Since 8218 > 5646, we apply the division lemma to 8218 and 5646, to get

8218 = 5646 x 1 + 2572

Step 2: Since the reminder 5646 ≠ 0, we apply division lemma to 2572 and 5646, to get

5646 = 2572 x 2 + 502

Step 3: We consider the new divisor 2572 and the new remainder 502, and apply the division lemma to get

2572 = 502 x 5 + 62

We consider the new divisor 502 and the new remainder 62,and apply the division lemma to get

502 = 62 x 8 + 6

We consider the new divisor 62 and the new remainder 6,and apply the division lemma to get

62 = 6 x 10 + 2

We consider the new divisor 6 and the new remainder 2,and apply the division lemma to get

6 = 2 x 3 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 8218 and 5646 is 2

Notice that 2 = HCF(6,2) = HCF(62,6) = HCF(502,62) = HCF(2572,502) = HCF(5646,2572) = HCF(8218,5646) .

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

Step 1: Since 74303 > 2, we apply the division lemma to 74303 and 2, to get

74303 = 2 x 37151 + 1

Step 2: Since the reminder 2 ≠ 0, we apply division lemma to 1 and 2, 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 2 and 74303 is 1

Notice that 1 = HCF(2,1) = HCF(74303,2) .

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Frequently Asked Questions on HCF of 8218, 5646, 74303 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 8218, 5646, 74303?

Answer: HCF of 8218, 5646, 74303 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 8218, 5646, 74303 using Euclid's Algorithm?

Answer: For arbitrary numbers 8218, 5646, 74303 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.