Highest Common Factor of 1854, 5666, 14177 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 1854, 5666, 14177 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 1854, 5666, 14177 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 1854, 5666, 14177 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 1854, 5666, 14177 is 1.

HCF(1854, 5666, 14177) = 1

HCF of 1854, 5666, 14177 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 1854, 5666, 14177 is 1.

Highest Common Factor of 1854,5666,14177 using Euclid's algorithm

Highest Common Factor of 1854,5666,14177 is 1

Step 1: Since 5666 > 1854, we apply the division lemma to 5666 and 1854, to get

5666 = 1854 x 3 + 104

Step 2: Since the reminder 1854 ≠ 0, we apply division lemma to 104 and 1854, to get

1854 = 104 x 17 + 86

Step 3: We consider the new divisor 104 and the new remainder 86, and apply the division lemma to get

104 = 86 x 1 + 18

We consider the new divisor 86 and the new remainder 18,and apply the division lemma to get

86 = 18 x 4 + 14

We consider the new divisor 18 and the new remainder 14,and apply the division lemma to get

18 = 14 x 1 + 4

We consider the new divisor 14 and the new remainder 4,and apply the division lemma to get

14 = 4 x 3 + 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 1854 and 5666 is 2

Notice that 2 = HCF(4,2) = HCF(14,4) = HCF(18,14) = HCF(86,18) = HCF(104,86) = HCF(1854,104) = HCF(5666,1854) .

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

Step 1: Since 14177 > 2, we apply the division lemma to 14177 and 2, to get

14177 = 2 x 7088 + 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 14177 is 1

Notice that 1 = HCF(2,1) = HCF(14177,2) .

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Frequently Asked Questions on HCF of 1854, 5666, 14177 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 1854, 5666, 14177?

Answer: HCF of 1854, 5666, 14177 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 1854, 5666, 14177 using Euclid's Algorithm?

Answer: For arbitrary numbers 1854, 5666, 14177 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.