Highest Common Factor of 7344, 2889, 37874 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 7344, 2889, 37874 i.e. 1 the largest integer that leaves a remainder zero for all numbers.

HCF of 7344, 2889, 37874 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 7344, 2889, 37874 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 7344, 2889, 37874 is 1.

HCF(7344, 2889, 37874) = 1

HCF of 7344, 2889, 37874 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 7344, 2889, 37874 is 1.

Highest Common Factor of 7344,2889,37874 using Euclid's algorithm

Highest Common Factor of 7344,2889,37874 is 1

Step 1: Since 7344 > 2889, we apply the division lemma to 7344 and 2889, to get

7344 = 2889 x 2 + 1566

Step 2: Since the reminder 2889 ≠ 0, we apply division lemma to 1566 and 2889, to get

2889 = 1566 x 1 + 1323

Step 3: We consider the new divisor 1566 and the new remainder 1323, and apply the division lemma to get

1566 = 1323 x 1 + 243

We consider the new divisor 1323 and the new remainder 243,and apply the division lemma to get

1323 = 243 x 5 + 108

We consider the new divisor 243 and the new remainder 108,and apply the division lemma to get

243 = 108 x 2 + 27

We consider the new divisor 108 and the new remainder 27,and apply the division lemma to get

108 = 27 x 4 + 0

The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 27, the HCF of 7344 and 2889 is 27

Notice that 27 = HCF(108,27) = HCF(243,108) = HCF(1323,243) = HCF(1566,1323) = HCF(2889,1566) = HCF(7344,2889) .

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

Step 1: Since 37874 > 27, we apply the division lemma to 37874 and 27, to get

37874 = 27 x 1402 + 20

Step 2: Since the reminder 27 ≠ 0, we apply division lemma to 20 and 27, to get

27 = 20 x 1 + 7

Step 3: We consider the new divisor 20 and the new remainder 7, and apply the division lemma to get

20 = 7 x 2 + 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 27 and 37874 is 1

Notice that 1 = HCF(6,1) = HCF(7,6) = HCF(20,7) = HCF(27,20) = HCF(37874,27) .

HCF using Euclid's Algorithm Calculation Examples

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

Frequently Asked Questions on HCF of 7344, 2889, 37874 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 7344, 2889, 37874?

Answer: HCF of 7344, 2889, 37874 is 1 the largest number that divides all the numbers leaving a remainder zero.

3. How to find HCF of 7344, 2889, 37874 using Euclid's Algorithm?

Answer: For arbitrary numbers 7344, 2889, 37874 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.