How to Find GCF of 5577/428, 4199/289?

GCF of 5577/428, 4199/289

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 5577/428, 4199/289 i.e 13/123692 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5577/428, 4199/289.

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 5577/428,4199/289?

Given fractions are 5577/428,4199/289

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 5577/428,4199/289, numerators are 5577,4199

Denominators are 428,289

The GCF of 5577,4199 is 13 .

LCM of 428,289 is 123692.

The greatest common factor of 5577/428,4199/289 = [GCF of 5577,4199]/[LCM of 428,289]= 13/123692

Therefore, the GCF of 5577/428,4199/289 is 13/123692.

Greatest Common Factor of 5577,4199

To find the highest common factor of 5577,4199, we have to find the factors of both numbers and list the highest common factor.

The factors of 5577 are 1, 3, 11, 13, 33, 39, 143, 169, 429, 507, 1859, 5577

The factors of 4199 are 1, 13, 17, 19, 221, 247, 323, 4199

The HCF of 5577,4199 is 13.

Lets's calculate GCF of 5577,4199

Greatest Common Factor (GCF) of 5577,4199 By Common Division

13	5577, 4199
	429, 323

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

Greatest Common Factor of 5577,4199 By Matching Biggest Common Factor Method

Now, list down the factors of 5577

1,3,11,13,33,39,143,169,429,507,1859,5577

Now, list down the factors of 4199

1,13,17,19,221,247,323,4199

Greatest Common Factor

We found the factors 5577,4199 . The biggest common factor number is the GCF number.
So the greatest common factor 5577,4199 is 13.

Lets's calculate LCM of 428,289

Lowest Common Multiple of 428,289 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 123692

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/123692

Therefore, the GCF of Fractions 5577/428,4199/289 is 13/123692

Least Common Multiple of 428,289 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 428,289 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(428,289) = 1

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

GCF(428,289) x common factors =1 x 1 = 1

LCM(428,289) = ( 428 × 289 ) / 1

LCM(428,289) = 123692 / 1

LCM(428,289) = 123692

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FAQs on GCF of Fractions of 5577/428, 4199/289

1. What is the HCF of 5577,4199?

The HCF of 5577,4199 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 5577/428, 4199/289?

Answer: GCF of Numerators as per given numbers 5577/428, 4199/289 is

GCF of Numerators i.e. for 5577,4199 is 13

LCM of denominators i.e. for 428,289 is 123692.

Thus, GCF of Fractions is 13/123692.Finally, GCF of Fractions for 5577/428, 4199/289 is 13/123692.