How to Find GCF of 5341/352, 7278/784?

GCF of 5341/352, 7278/784

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 5341/352, 7278/784 i.e 1/17248 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5341/352, 7278/784.

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 5341/352,7278/784?

Given fractions are 5341/352,7278/784

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 5341/352,7278/784, numerators are 5341,7278

Denominators are 352,784

The GCF of 5341,7278 is 1 .

LCM of 352,784 is 17248.

The greatest common factor of 5341/352,7278/784 = [GCF of 5341,7278]/[LCM of 352,784]= 1/17248

Therefore, the GCF of 5341/352,7278/784 is 1/17248.

Greatest Common Factor of 5341,7278

To find the highest common factor of 5341,7278, we have to find the factors of both numbers and list the highest common factor.

The factors of 5341 are 1, 7, 49, 109, 763, 5341

The factors of 7278 are 1, 2, 3, 6, 1213, 2426, 3639, 7278

The HCF of 5341,7278 is 1.

Lets's calculate GCF of 5341,7278

Greatest Common Factor (GCF) of 5341,7278 By Common Division

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

Greatest Common Factor of 5341,7278 By Matching Biggest Common Factor Method

Now, list down the factors of 5341

1,7,49,109,763,5341

Now, list down the factors of 7278

1,2,3,6,1213,2426,3639,7278

Greatest Common Factor

We found the factors 5341,7278 . The biggest common factor number is the GCF number.
So the greatest common factor 5341,7278 is 1.

Lets's calculate LCM of 352,784

Lowest Common Multiple of 352,784 using Common Division

2	352, 784
2	176, 392
2	88, 196
2	44, 98
	22, 49

∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 22 x 49 = 17248

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17248

Therefore, the GCF of Fractions 5341/352,7278/784 is 1/17248

Least Common Multiple of 352,784 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 352,784 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(352,784) = 16

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

GCF(352,784) x common factors =16 x 1 = 16

LCM(352,784) = ( 352 × 784 ) / 16

LCM(352,784) = 275968 / 16

LCM(352,784) = 17248

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FAQs on GCF of Fractions of 5341/352, 7278/784

1. What is the HCF of 5341,7278?

The HCF of 5341,7278 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 5341/352, 7278/784?

Answer: GCF of Numerators as per given numbers 5341/352, 7278/784 is

GCF of Numerators i.e. for 5341,7278 is 1

LCM of denominators i.e. for 352,784 is 17248.

Thus, GCF of Fractions is 1/17248.Finally, GCF of Fractions for 5341/352, 7278/784 is 1/17248.