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GCF of 403/78, 741/758

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 403/78, 741/758 i.e 13/29562 easily. The following is the detailed procedure to determine the greatest common factor of fractions 403/78, 741/758.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

GCF of:

What is the GCF of 403/78,741/758?

Given fractions are 403/78,741/758

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 403/78,741/758, numerators are 403,741

Denominators are 78,758

The GCF of 403,741 is 13 .

LCM of 78,758 is 29562.

The greatest common factor of 403/78,741/758 = [GCF of 403,741]/[LCM of 78,758]= 13/29562

Therefore, the GCF of 403/78,741/758 is 13/29562.

Greatest Common Factor of 403,741

To find the highest common factor of 403,741, we have to find the factors of both numbers and list the highest common factor.

The factors of 403 are 1, 13, 31, 403

The factors of 741 are 1, 3, 13, 19, 39, 57, 247, 741

The HCF of 403,741 is 13.

Lets's calculate GCF of 403,741

Greatest Common Factor (GCF) of 403,741 By Common Division

13 403, 741
31, 57

∴ So the GCF of the given numbers is 13 = 13

Greatest Common Factor of 403,741 By Matching Biggest Common Factor Method

Greatest Common Factor of 403,741 By Matching Biggest Common Factor Method

Now, list down the factors of 403

:

1,13,31,403

Now, list down the factors of 741

:

1,3,13,19,39,57,247,741

Greatest Common Factor

We found the factors 403,741 . The biggest common factor number is the GCF number.
So the greatest common factor 403,741 is 13.

Lets's calculate LCM of 78,758

Lowest Common Multiple of 78,758 using Common Division

2 78, 758
39, 379

∴ So the LCM of the given numbers is 2 x 39 x 379 = 29562

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/29562

Therefore, the GCF of Fractions 403/78,741/758 is 13/29562

Least Common Multiple of 78,758 with GCF Formula

Least Common Multiple of 78,758 with GCF Formula

The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 78,758 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(78,758) = 2

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

GCF(78,758) x common factors =2 x 1 = 2

LCM(78,758) = ( 78 × 758 ) / 2

LCM(78,758) = 59124 / 2

LCM(78,758) = 29562


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FAQs on GCF of Fractions of 403/78, 741/758

1. What is the HCF of 403,741?

The HCF of 403,741 is 13

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 403/78, 741/758?

Answer: GCF of Numerators as per given numbers 403/78, 741/758 is

GCF of Numerators i.e. for 403,741 is 13

LCM of denominators i.e. for 78,758 is 29562.

Thus, GCF of Fractions is 13/29562.Finally, GCF of Fractions for 403/78, 741/758 is 13/29562.