How to Find GCF of 2103/784, 2233/7600?

GCF of 2103/784, 2233/7600

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 2103/784, 2233/7600 i.e 1/372400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2103/784, 2233/7600.

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 2103/784,2233/7600?

Given fractions are 2103/784,2233/7600

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 2103/784,2233/7600, numerators are 2103,2233

Denominators are 784,7600

The GCF of 2103,2233 is 1 .

LCM of 784,7600 is 372400.

The greatest common factor of 2103/784,2233/7600 = [GCF of 2103,2233]/[LCM of 784,7600]= 1/372400

Therefore, the GCF of 2103/784,2233/7600 is 1/372400.

Greatest Common Factor of 2103,2233

To find the highest common factor of 2103,2233, we have to find the factors of both numbers and list the highest common factor.

The factors of 2103 are 1, 3, 701, 2103

The factors of 2233 are 1, 7, 11, 29, 77, 203, 319, 2233

The HCF of 2103,2233 is 1.

Lets's calculate GCF of 2103,2233

Greatest Common Factor (GCF) of 2103,2233 By Common Division

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

Greatest Common Factor of 2103,2233 By Matching Biggest Common Factor Method

Now, list down the factors of 2103

1,3,701,2103

Now, list down the factors of 2233

1,7,11,29,77,203,319,2233

Greatest Common Factor

We found the factors 2103,2233 . The biggest common factor number is the GCF number.
So the greatest common factor 2103,2233 is 1.

Lets's calculate LCM of 784,7600

Lowest Common Multiple of 784,7600 using Common Division

2	784, 7600
2	392, 3800
2	196, 1900
2	98, 950
	49, 475

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 49 x 475 = 372400

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/372400

Therefore, the GCF of Fractions 2103/784,2233/7600 is 1/372400

Least Common Multiple of 784,7600 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 784,7600 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(784,7600) = 16

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

GCF(784,7600) x common factors =16 x 1 = 16

LCM(784,7600) = ( 784 × 7600 ) / 16

LCM(784,7600) = 5958400 / 16

LCM(784,7600) = 372400

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FAQs on GCF of Fractions of 2103/784, 2233/7600

1. What is the HCF of 2103,2233?

The HCF of 2103,2233 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 2103/784, 2233/7600?

Answer: GCF of Numerators as per given numbers 2103/784, 2233/7600 is

GCF of Numerators i.e. for 2103,2233 is 1

LCM of denominators i.e. for 784,7600 is 372400.

Thus, GCF of Fractions is 1/372400.Finally, GCF of Fractions for 2103/784, 2233/7600 is 1/372400.