Highest Common Factor of 2741, 4148 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 2741, 4148 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 2741, 4148 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 2741, 4148 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 2741, 4148 is 1.

HCF(2741, 4148) = 1

HCF of 2741, 4148 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 2741, 4148 is 1.

Highest Common Factor of 2741,4148 using Euclid's algorithm

Highest Common Factor of 2741,4148 is 1

Step 1: Since 4148 > 2741, we apply the division lemma to 4148 and 2741, to get

4148 = 2741 x 1 + 1407

Step 2: Since the reminder 2741 ≠ 0, we apply division lemma to 1407 and 2741, to get

2741 = 1407 x 1 + 1334

Step 3: We consider the new divisor 1407 and the new remainder 1334, and apply the division lemma to get

1407 = 1334 x 1 + 73

We consider the new divisor 1334 and the new remainder 73,and apply the division lemma to get

1334 = 73 x 18 + 20

We consider the new divisor 73 and the new remainder 20,and apply the division lemma to get

73 = 20 x 3 + 13

We consider the new divisor 20 and the new remainder 13,and apply the division lemma to get

20 = 13 x 1 + 7

We consider the new divisor 13 and the new remainder 7,and apply the division lemma to get

13 = 7 x 1 + 6

We consider the new divisor 7 and the new remainder 6,and apply the division lemma to get

7 = 6 x 1 + 1

We consider the new divisor 6 and the new remainder 1,and apply the division lemma to get

6 = 1 x 6 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 2741 and 4148 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(13,7) = HCF(20,13) = HCF(73,20) = HCF(1334,73) = HCF(1407,1334) = HCF(2741,1407) = HCF(4148,2741) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 2741, 4148 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 2741, 4148?

Answer: HCF of 2741, 4148 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 2741, 4148 using Euclid's Algorithm?

Answer: For arbitrary numbers 2741, 4148 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.