Highest Common Factor of 2154, 4089 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 2154, 4089 i.e. 3 the largest integer that leaves a remainder zero for all numbers.

HCF of 2154, 4089 is 3 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 2154, 4089 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 2154, 4089 is 3.

HCF(2154, 4089) = 3

HCF of 2154, 4089 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 2154, 4089 is 3.

Highest Common Factor of 2154,4089 using Euclid's algorithm

Highest Common Factor of 2154,4089 is 3

Step 1: Since 4089 > 2154, we apply the division lemma to 4089 and 2154, to get

4089 = 2154 x 1 + 1935

Step 2: Since the reminder 2154 ≠ 0, we apply division lemma to 1935 and 2154, to get

2154 = 1935 x 1 + 219

Step 3: We consider the new divisor 1935 and the new remainder 219, and apply the division lemma to get

1935 = 219 x 8 + 183

We consider the new divisor 219 and the new remainder 183,and apply the division lemma to get

219 = 183 x 1 + 36

We consider the new divisor 183 and the new remainder 36,and apply the division lemma to get

183 = 36 x 5 + 3

We consider the new divisor 36 and the new remainder 3,and apply the division lemma to get

36 = 3 x 12 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 2154 and 4089 is 3

Notice that 3 = HCF(36,3) = HCF(183,36) = HCF(219,183) = HCF(1935,219) = HCF(2154,1935) = HCF(4089,2154) .

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Frequently Asked Questions on HCF of 2154, 4089 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 2154, 4089?

Answer: HCF of 2154, 4089 is 3 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2154, 4089 using Euclid's Algorithm?

Answer: For arbitrary numbers 2154, 4089 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.