How to Find GCF of 2353/288, 6175/1400?

GCF of 2353/288, 6175/1400

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 2353/288, 6175/1400 i.e 13/50400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2353/288, 6175/1400.

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 2353/288,6175/1400?

Given fractions are 2353/288,6175/1400

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 2353/288,6175/1400, numerators are 2353,6175

Denominators are 288,1400

The GCF of 2353,6175 is 13 .

LCM of 288,1400 is 50400.

The greatest common factor of 2353/288,6175/1400 = [GCF of 2353,6175]/[LCM of 288,1400]= 13/50400

Therefore, the GCF of 2353/288,6175/1400 is 13/50400.

Greatest Common Factor of 2353,6175

To find the highest common factor of 2353,6175, we have to find the factors of both numbers and list the highest common factor.

The factors of 2353 are 1, 13, 181, 2353

The factors of 6175 are 1, 5, 13, 19, 25, 65, 95, 247, 325, 475, 1235, 6175

The HCF of 2353,6175 is 13.

Lets's calculate GCF of 2353,6175

Greatest Common Factor (GCF) of 2353,6175 By Common Division

13	2353, 6175
	181, 475

∴ So the GCF of the given numbers is 13 = 13

Greatest Common Factor of 2353,6175 By Matching Biggest Common Factor Method

Now, list down the factors of 2353

1,13,181,2353

Now, list down the factors of 6175

1,5,13,19,25,65,95,247,325,475,1235,6175

Greatest Common Factor

We found the factors 2353,6175 . The biggest common factor number is the GCF number.
So the greatest common factor 2353,6175 is 13.

Lets's calculate LCM of 288,1400

Lowest Common Multiple of 288,1400 using Common Division

2	288, 1400
2	144, 700
2	72, 350
	36, 175

∴ So the LCM of the given numbers is 2 x 2 x 2 x 36 x 175 = 50400

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/50400

Therefore, the GCF of Fractions 2353/288,6175/1400 is 13/50400

Least Common Multiple of 288,1400 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 288,1400 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(288,1400) = 8

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

GCF(288,1400) x common factors =8 x 1 = 8

LCM(288,1400) = ( 288 × 1400 ) / 8

LCM(288,1400) = 403200 / 8

LCM(288,1400) = 50400

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FAQs on GCF of Fractions of 2353/288, 6175/1400

1. What is the HCF of 2353,6175?

The HCF of 2353,6175 is 13

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 2353/288, 6175/1400?

Answer: GCF of Numerators as per given numbers 2353/288, 6175/1400 is

GCF of Numerators i.e. for 2353,6175 is 13

LCM of denominators i.e. for 288,1400 is 50400.

Thus, GCF of Fractions is 13/50400.Finally, GCF of Fractions for 2353/288, 6175/1400 is 13/50400.