How to Find GCF of 762/297, 5824/194?

GCF of 762/297, 5824/194

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 762/297, 5824/194 i.e 2/57618 easily. The following is the detailed procedure to determine the greatest common factor of fractions 762/297, 5824/194.

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 762/297,5824/194?

Given fractions are 762/297,5824/194

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 762/297,5824/194, numerators are 762,5824

Denominators are 297,194

The GCF of 762,5824 is 2 .

LCM of 297,194 is 57618.

The greatest common factor of 762/297,5824/194 = [GCF of 762,5824]/[LCM of 297,194]= 2/57618

Therefore, the GCF of 762/297,5824/194 is 2/57618.

Greatest Common Factor of 762,5824

To find the highest common factor of 762,5824, we have to find the factors of both numbers and list the highest common factor.

The factors of 762 are 1, 2, 3, 6, 127, 254, 381, 762

The factors of 5824 are 1, 2, 4, 7, 8, 13, 14, 16, 26, 28, 32, 52, 56, 64, 91, 104, 112, 182, 208, 224, 364, 416, 448, 728, 832, 1456, 2912, 5824

The HCF of 762,5824 is 2.

Lets's calculate GCF of 762,5824

Greatest Common Factor (GCF) of 762,5824 By Common Division

2	762, 5824
	381, 2912

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 762,5824 By Matching Biggest Common Factor Method

Now, list down the factors of 762

1,2,3,6,127,254,381,762

Now, list down the factors of 5824

1,2,4,7,8,13,14,16,26,28,32,52,56,64,91,104,112,182,208,224,364,416,448,728,832,1456,2912,5824

Greatest Common Factor

We found the factors 762,5824 . The biggest common factor number is the GCF number.
So the greatest common factor 762,5824 is 2.

Lets's calculate LCM of 297,194

Lowest Common Multiple of 297,194 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 57618

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/57618

Therefore, the GCF of Fractions 762/297,5824/194 is 2/57618

Least Common Multiple of 297,194 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 297,194 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(297,194) = 1

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

GCF(297,194) x common factors =1 x 1 = 1

LCM(297,194) = ( 297 × 194 ) / 1

LCM(297,194) = 57618 / 1

LCM(297,194) = 57618

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FAQs on GCF of Fractions of 762/297, 5824/194

1. What is the HCF of 762,5824?

The HCF of 762,5824 is 2

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 762/297, 5824/194?

Answer: GCF of Numerators as per given numbers 762/297, 5824/194 is

GCF of Numerators i.e. for 762,5824 is 2

LCM of denominators i.e. for 297,194 is 57618.

Thus, GCF of Fractions is 2/57618.Finally, GCF of Fractions for 762/297, 5824/194 is 2/57618.