Highest Common Factor of 6554, 3814 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 6554, 3814 i.e. 2 the largest integer that leaves a remainder zero for all numbers.

HCF of 6554, 3814 is 2 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 6554, 3814 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 6554, 3814 is 2.

HCF(6554, 3814) = 2

HCF of 6554, 3814 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 6554, 3814 is 2.

Highest Common Factor of 6554,3814 using Euclid's algorithm

Highest Common Factor of 6554,3814 is 2

Step 1: Since 6554 > 3814, we apply the division lemma to 6554 and 3814, to get

6554 = 3814 x 1 + 2740

Step 2: Since the reminder 3814 ≠ 0, we apply division lemma to 2740 and 3814, to get

3814 = 2740 x 1 + 1074

Step 3: We consider the new divisor 2740 and the new remainder 1074, and apply the division lemma to get

2740 = 1074 x 2 + 592

We consider the new divisor 1074 and the new remainder 592,and apply the division lemma to get

1074 = 592 x 1 + 482

We consider the new divisor 592 and the new remainder 482,and apply the division lemma to get

592 = 482 x 1 + 110

We consider the new divisor 482 and the new remainder 110,and apply the division lemma to get

482 = 110 x 4 + 42

We consider the new divisor 110 and the new remainder 42,and apply the division lemma to get

110 = 42 x 2 + 26

We consider the new divisor 42 and the new remainder 26,and apply the division lemma to get

42 = 26 x 1 + 16

We consider the new divisor 26 and the new remainder 16,and apply the division lemma to get

26 = 16 x 1 + 10

We consider the new divisor 16 and the new remainder 10,and apply the division lemma to get

16 = 10 x 1 + 6

We consider the new divisor 10 and the new remainder 6,and apply the division lemma to get

10 = 6 x 1 + 4

We consider the new divisor 6 and the new remainder 4,and apply the division lemma to get

6 = 4 x 1 + 2

We consider the new divisor 4 and the new remainder 2,and apply the division lemma to get

4 = 2 x 2 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 6554 and 3814 is 2

Notice that 2 = HCF(4,2) = HCF(6,4) = HCF(10,6) = HCF(16,10) = HCF(26,16) = HCF(42,26) = HCF(110,42) = HCF(482,110) = HCF(592,482) = HCF(1074,592) = HCF(2740,1074) = HCF(3814,2740) = HCF(6554,3814) .

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Frequently Asked Questions on HCF of 6554, 3814 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 6554, 3814?

Answer: HCF of 6554, 3814 is 2 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 6554, 3814 using Euclid's Algorithm?

Answer: For arbitrary numbers 6554, 3814 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.