Highest Common Factor of 2339, 4472, 32128 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 2339, 4472, 32128 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2339, 4472, 32128 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 2339, 4472, 32128 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 2339, 4472, 32128 is 1.

HCF(2339, 4472, 32128) = 1

HCF of 2339, 4472, 32128 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 2339, 4472, 32128 is 1.

Highest Common Factor of 2339,4472,32128 using Euclid's algorithm

Highest Common Factor of 2339,4472,32128 is 1

Step 1: Since 4472 > 2339, we apply the division lemma to 4472 and 2339, to get

4472 = 2339 x 1 + 2133

Step 2: Since the reminder 2339 ≠ 0, we apply division lemma to 2133 and 2339, to get

2339 = 2133 x 1 + 206

Step 3: We consider the new divisor 2133 and the new remainder 206, and apply the division lemma to get

2133 = 206 x 10 + 73

We consider the new divisor 206 and the new remainder 73,and apply the division lemma to get

206 = 73 x 2 + 60

We consider the new divisor 73 and the new remainder 60,and apply the division lemma to get

73 = 60 x 1 + 13

We consider the new divisor 60 and the new remainder 13,and apply the division lemma to get

60 = 13 x 4 + 8

We consider the new divisor 13 and the new remainder 8,and apply the division lemma to get

13 = 8 x 1 + 5

We consider the new divisor 8 and the new remainder 5,and apply the division lemma to get

8 = 5 x 1 + 3

We consider the new divisor 5 and the new remainder 3,and apply the division lemma to get

5 = 3 x 1 + 2

We consider the new divisor 3 and the new remainder 2,and apply the division lemma to get

3 = 2 x 1 + 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 2339 and 4472 is 1

Notice that 1 = HCF(2,1) = HCF(3,2) = HCF(5,3) = HCF(8,5) = HCF(13,8) = HCF(60,13) = HCF(73,60) = HCF(206,73) = HCF(2133,206) = HCF(2339,2133) = HCF(4472,2339) .

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

Step 1: Since 32128 > 1, we apply the division lemma to 32128 and 1, to get

32128 = 1 x 32128 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 32128 is 1

Notice that 1 = HCF(32128,1) .

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Frequently Asked Questions on HCF of 2339, 4472, 32128 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 2339, 4472, 32128?

Answer: HCF of 2339, 4472, 32128 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2339, 4472, 32128 using Euclid's Algorithm?

Answer: For arbitrary numbers 2339, 4472, 32128 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.