Highest Common Factor of 1906, 9123, 53904 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 1906, 9123, 53904 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1906, 9123, 53904 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 1906, 9123, 53904 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 1906, 9123, 53904 is 1.

HCF(1906, 9123, 53904) = 1

HCF of 1906, 9123, 53904 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 1906, 9123, 53904 is 1.

Highest Common Factor of 1906,9123,53904 using Euclid's algorithm

Highest Common Factor of 1906,9123,53904 is 1

Step 1: Since 9123 > 1906, we apply the division lemma to 9123 and 1906, to get

9123 = 1906 x 4 + 1499

Step 2: Since the reminder 1906 ≠ 0, we apply division lemma to 1499 and 1906, to get

1906 = 1499 x 1 + 407

Step 3: We consider the new divisor 1499 and the new remainder 407, and apply the division lemma to get

1499 = 407 x 3 + 278

We consider the new divisor 407 and the new remainder 278,and apply the division lemma to get

407 = 278 x 1 + 129

We consider the new divisor 278 and the new remainder 129,and apply the division lemma to get

278 = 129 x 2 + 20

We consider the new divisor 129 and the new remainder 20,and apply the division lemma to get

129 = 20 x 6 + 9

We consider the new divisor 20 and the new remainder 9,and apply the division lemma to get

20 = 9 x 2 + 2

We consider the new divisor 9 and the new remainder 2,and apply the division lemma to get

9 = 2 x 4 + 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 1906 and 9123 is 1

Notice that 1 = HCF(2,1) = HCF(9,2) = HCF(20,9) = HCF(129,20) = HCF(278,129) = HCF(407,278) = HCF(1499,407) = HCF(1906,1499) = HCF(9123,1906) .

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

Step 1: Since 53904 > 1, we apply the division lemma to 53904 and 1, to get

53904 = 1 x 53904 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 53904 is 1

Notice that 1 = HCF(53904,1) .

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Frequently Asked Questions on HCF of 1906, 9123, 53904 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 1906, 9123, 53904?

Answer: HCF of 1906, 9123, 53904 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1906, 9123, 53904 using Euclid's Algorithm?

Answer: For arbitrary numbers 1906, 9123, 53904 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.