How to Find GCF of 7831/296, 1353/1768?

GCF of 7831/296, 1353/1768

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 7831/296, 1353/1768 i.e 41/65416 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7831/296, 1353/1768.

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 7831/296,1353/1768?

Given fractions are 7831/296,1353/1768

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 7831/296,1353/1768, numerators are 7831,1353

Denominators are 296,1768

The GCF of 7831,1353 is 41 .

LCM of 296,1768 is 65416.

The greatest common factor of 7831/296,1353/1768 = [GCF of 7831,1353]/[LCM of 296,1768]= 41/65416

Therefore, the GCF of 7831/296,1353/1768 is 41/65416.

Greatest Common Factor of 7831,1353

To find the highest common factor of 7831,1353, we have to find the factors of both numbers and list the highest common factor.

The factors of 7831 are 1, 41, 191, 7831

The factors of 1353 are 1, 3, 11, 33, 41, 123, 451, 1353

The HCF of 7831,1353 is 41.

Lets's calculate GCF of 7831,1353

Greatest Common Factor (GCF) of 7831,1353 By Common Division

41	7831, 1353
	191, 33

∴ So the GCF of the given numbers is 41 = 41

Greatest Common Factor of 7831,1353 By Matching Biggest Common Factor Method

Now, list down the factors of 7831

1,41,191,7831

Now, list down the factors of 1353

1,3,11,33,41,123,451,1353

Greatest Common Factor

We found the factors 7831,1353 . The biggest common factor number is the GCF number.
So the greatest common factor 7831,1353 is 41.

Lets's calculate LCM of 296,1768

Lowest Common Multiple of 296,1768 using Common Division

2	296, 1768
2	148, 884
2	74, 442
	37, 221

∴ So the LCM of the given numbers is 2 x 2 x 2 x 37 x 221 = 65416

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 41/65416

Therefore, the GCF of Fractions 7831/296,1353/1768 is 41/65416

Least Common Multiple of 296,1768 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 296,1768 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(296,1768) = 8

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

GCF(296,1768) x common factors =8 x 1 = 8

LCM(296,1768) = ( 296 × 1768 ) / 8

LCM(296,1768) = 523328 / 8

LCM(296,1768) = 65416

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FAQs on GCF of Fractions of 7831/296, 1353/1768

1. What is the HCF of 7831,1353?

The HCF of 7831,1353 is 41

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 7831/296, 1353/1768?

Answer: GCF of Numerators as per given numbers 7831/296, 1353/1768 is

GCF of Numerators i.e. for 7831,1353 is 41

LCM of denominators i.e. for 296,1768 is 65416.

Thus, GCF of Fractions is 41/65416.Finally, GCF of Fractions for 7831/296, 1353/1768 is 41/65416.