How to Find GCF of 2829/300, 2140/4324?

GCF of 2829/300, 2140/4324

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 2829/300, 2140/4324 i.e 1/324300 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2829/300, 2140/4324.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 2829/300,2140/4324?

Given fractions are 2829/300,2140/4324

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 2829/300,2140/4324, numerators are 2829,2140

Denominators are 300,4324

The GCF of 2829,2140 is 1 .

LCM of 300,4324 is 324300.

The greatest common factor of 2829/300,2140/4324 = [GCF of 2829,2140]/[LCM of 300,4324]= 1/324300

Therefore, the GCF of 2829/300,2140/4324 is 1/324300.

Greatest Common Factor of 2829,2140

To find the highest common factor of 2829,2140, we have to find the factors of both numbers and list the highest common factor.

The factors of 2829 are 1, 3, 23, 41, 69, 123, 943, 2829

The factors of 2140 are 1, 2, 4, 5, 10, 20, 107, 214, 428, 535, 1070, 2140

The HCF of 2829,2140 is 1.

Lets's calculate GCF of 2829,2140

Greatest Common Factor (GCF) of 2829,2140 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 2829,2140 By Matching Biggest Common Factor Method

Now, list down the factors of 2829

1,3,23,41,69,123,943,2829

Now, list down the factors of 2140

1,2,4,5,10,20,107,214,428,535,1070,2140

Greatest Common Factor

We found the factors 2829,2140 . The biggest common factor number is the GCF number.
So the greatest common factor 2829,2140 is 1.

Lets's calculate LCM of 300,4324

Lowest Common Multiple of 300,4324 using Common Division

2	300, 4324
2	150, 2162
	75, 1081

∴ So the LCM of the given numbers is 2 x 2 x 75 x 1081 = 324300

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/324300

Therefore, the GCF of Fractions 2829/300,2140/4324 is 1/324300

Least Common Multiple of 300,4324 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 300,4324 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(300,4324) = 4

common factors(in case of two or more numbers have common factors) = 1

GCF(300,4324) x common factors =4 x 1 = 4

LCM(300,4324) = ( 300 × 4324 ) / 4

LCM(300,4324) = 1297200 / 4

LCM(300,4324) = 324300

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FAQs on GCF of Fractions of 2829/300, 2140/4324

1. What is the HCF of 2829,2140?

The HCF of 2829,2140 is 1

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 2829/300, 2140/4324?

Answer: GCF of Numerators as per given numbers 2829/300, 2140/4324 is

GCF of Numerators i.e. for 2829,2140 is 1

LCM of denominators i.e. for 300,4324 is 324300.

Thus, GCF of Fractions is 1/324300.Finally, GCF of Fractions for 2829/300, 2140/4324 is 1/324300.