How to Find GCF of 768/274, 908/653?

GCF of 768/274, 908/653

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 768/274, 908/653 i.e 4/178922 easily. The following is the detailed procedure to determine the greatest common factor of fractions 768/274, 908/653.

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 768/274,908/653?

Given fractions are 768/274,908/653

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 768/274,908/653, numerators are 768,908

Denominators are 274,653

The GCF of 768,908 is 4 .

LCM of 274,653 is 178922.

The greatest common factor of 768/274,908/653 = [GCF of 768,908]/[LCM of 274,653]= 4/178922

Therefore, the GCF of 768/274,908/653 is 4/178922.

Greatest Common Factor of 768,908

To find the highest common factor of 768,908, we have to find the factors of both numbers and list the highest common factor.

The factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768

The factors of 908 are 1, 2, 4, 227, 454, 908

The HCF of 768,908 is 4.

Lets's calculate GCF of 768,908

Greatest Common Factor (GCF) of 768,908 By Common Division

2	768, 908
2	384, 454
	192, 227

∴ So the GCF of the given numbers is 2 x 2 = 4

Greatest Common Factor of 768,908 By Matching Biggest Common Factor Method

Now, list down the factors of 768

1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,768

Now, list down the factors of 908

1,2,4,227,454,908

Greatest Common Factor

We found the factors 768,908 . The biggest common factor number is the GCF number.
So the greatest common factor 768,908 is 4.

Lets's calculate LCM of 274,653

Lowest Common Multiple of 274,653 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 178922

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/178922

Therefore, the GCF of Fractions 768/274,908/653 is 4/178922

Least Common Multiple of 274,653 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 274,653 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(274,653) = 1

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

GCF(274,653) x common factors =1 x 1 = 1

LCM(274,653) = ( 274 × 653 ) / 1

LCM(274,653) = 178922 / 1

LCM(274,653) = 178922

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FAQs on GCF of Fractions of 768/274, 908/653

1. What is the HCF of 768,908?

The HCF of 768,908 is 4

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 768/274, 908/653?

Answer: GCF of Numerators as per given numbers 768/274, 908/653 is

GCF of Numerators i.e. for 768,908 is 4

LCM of denominators i.e. for 274,653 is 178922.

Thus, GCF of Fractions is 4/178922.Finally, GCF of Fractions for 768/274, 908/653 is 4/178922.