Highest Common Factor of 339, 2137, 1743 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 339, 2137, 1743 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 339, 2137, 1743 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 339, 2137, 1743 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 339, 2137, 1743 is 1.

HCF(339, 2137, 1743) = 1

HCF of 339, 2137, 1743 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 339, 2137, 1743 is 1.

Highest Common Factor of 339,2137,1743 using Euclid's algorithm

Highest Common Factor of 339,2137,1743 is 1

Step 1: Since 2137 > 339, we apply the division lemma to 2137 and 339, to get

2137 = 339 x 6 + 103

Step 2: Since the reminder 339 ≠ 0, we apply division lemma to 103 and 339, to get

339 = 103 x 3 + 30

Step 3: We consider the new divisor 103 and the new remainder 30, and apply the division lemma to get

103 = 30 x 3 + 13

We consider the new divisor 30 and the new remainder 13,and apply the division lemma to get

30 = 13 x 2 + 4

We consider the new divisor 13 and the new remainder 4,and apply the division lemma to get

13 = 4 x 3 + 1

We consider the new divisor 4 and the new remainder 1,and apply the division lemma to get

4 = 1 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 339 and 2137 is 1

Notice that 1 = HCF(4,1) = HCF(13,4) = HCF(30,13) = HCF(103,30) = HCF(339,103) = HCF(2137,339) .

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

Step 1: Since 1743 > 1, we apply the division lemma to 1743 and 1, to get

1743 = 1 x 1743 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 1 and 1743 is 1

Notice that 1 = HCF(1743,1) .

HCF using Euclid's Algorithm Calculation Examples

Here are some samples of HCF using Euclid's Algorithm calculations.

Frequently Asked Questions on HCF of 339, 2137, 1743 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 339, 2137, 1743?

Answer: HCF of 339, 2137, 1743 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 339, 2137, 1743 using Euclid's Algorithm?

Answer: For arbitrary numbers 339, 2137, 1743 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.