How to Find GCF of 51/104, 5474/2468?

GCF of 51/104, 5474/2468

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 51/104, 5474/2468 i.e 17/64168 easily. The following is the detailed procedure to determine the greatest common factor of fractions 51/104, 5474/2468.

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 51/104,5474/2468?

Given fractions are 51/104,5474/2468

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 51/104,5474/2468, numerators are 51,5474

Denominators are 104,2468

The GCF of 51,5474 is 17 .

LCM of 104,2468 is 64168.

The greatest common factor of 51/104,5474/2468 = [GCF of 51,5474]/[LCM of 104,2468]= 17/64168

Therefore, the GCF of 51/104,5474/2468 is 17/64168.

Greatest Common Factor of 51,5474

To find the highest common factor of 51,5474, we have to find the factors of both numbers and list the highest common factor.

The factors of 51 are 1, 3, 17, 51

The factors of 5474 are 1, 2, 7, 14, 17, 23, 34, 46, 119, 161, 238, 322, 391, 782, 2737, 5474

The HCF of 51,5474 is 17.

Lets's calculate GCF of 51,5474

Greatest Common Factor (GCF) of 51,5474 By Common Division

17	51, 5474
	3, 322

∴ So the GCF of the given numbers is 17 = 17

Greatest Common Factor of 51,5474 By Matching Biggest Common Factor Method

Now, list down the factors of 51

1,3,17,51

Now, list down the factors of 5474

1,2,7,14,17,23,34,46,119,161,238,322,391,782,2737,5474

Greatest Common Factor

We found the factors 51,5474 . The biggest common factor number is the GCF number.
So the greatest common factor 51,5474 is 17.

Lets's calculate LCM of 104,2468

Lowest Common Multiple of 104,2468 using Common Division

2	104, 2468
2	52, 1234
	26, 617

∴ So the LCM of the given numbers is 2 x 2 x 26 x 617 = 64168

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/64168

Therefore, the GCF of Fractions 51/104,5474/2468 is 17/64168

Least Common Multiple of 104,2468 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 104,2468 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(104,2468) = 4

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

GCF(104,2468) x common factors =4 x 1 = 4

LCM(104,2468) = ( 104 × 2468 ) / 4

LCM(104,2468) = 256672 / 4

LCM(104,2468) = 64168

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FAQs on GCF of Fractions of 51/104, 5474/2468

1. What is the HCF of 51,5474?

The HCF of 51,5474 is 17

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 51/104, 5474/2468?

Answer: GCF of Numerators as per given numbers 51/104, 5474/2468 is

GCF of Numerators i.e. for 51,5474 is 17

LCM of denominators i.e. for 104,2468 is 64168.

Thus, GCF of Fractions is 17/64168.Finally, GCF of Fractions for 51/104, 5474/2468 is 17/64168.