How to Find GCF of 738/766, 7688/370?

GCF of 738/766, 7688/370

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 738/766, 7688/370 i.e 2/141710 easily. The following is the detailed procedure to determine the greatest common factor of fractions 738/766, 7688/370.

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 738/766,7688/370?

Given fractions are 738/766,7688/370

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 738/766,7688/370, numerators are 738,7688

Denominators are 766,370

The GCF of 738,7688 is 2 .

LCM of 766,370 is 141710.

The greatest common factor of 738/766,7688/370 = [GCF of 738,7688]/[LCM of 766,370]= 2/141710

Therefore, the GCF of 738/766,7688/370 is 2/141710.

Greatest Common Factor of 738,7688

To find the highest common factor of 738,7688, we have to find the factors of both numbers and list the highest common factor.

The factors of 738 are 1, 2, 3, 6, 9, 18, 41, 82, 123, 246, 369, 738

The factors of 7688 are 1, 2, 4, 8, 31, 62, 124, 248, 961, 1922, 3844, 7688

The HCF of 738,7688 is 2.

Lets's calculate GCF of 738,7688

Greatest Common Factor (GCF) of 738,7688 By Common Division

2	738, 7688
	369, 3844

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

Greatest Common Factor of 738,7688 By Matching Biggest Common Factor Method

Now, list down the factors of 738

1,2,3,6,9,18,41,82,123,246,369,738

Now, list down the factors of 7688

1,2,4,8,31,62,124,248,961,1922,3844,7688

Greatest Common Factor

We found the factors 738,7688 . The biggest common factor number is the GCF number.
So the greatest common factor 738,7688 is 2.

Lets's calculate LCM of 766,370

Lowest Common Multiple of 766,370 using Common Division

2	766, 370
	383, 185

∴ So the LCM of the given numbers is 2 x 383 x 185 = 141710

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/141710

Therefore, the GCF of Fractions 738/766,7688/370 is 2/141710

Least Common Multiple of 766,370 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 766,370 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(766,370) = 2

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

GCF(766,370) x common factors =2 x 1 = 2

LCM(766,370) = ( 766 × 370 ) / 2

LCM(766,370) = 283420 / 2

LCM(766,370) = 141710

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 738/766, 7688/370

1. What is the HCF of 738,7688?

The HCF of 738,7688 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 738/766, 7688/370?

Answer: GCF of Numerators as per given numbers 738/766, 7688/370 is

GCF of Numerators i.e. for 738,7688 is 2

LCM of denominators i.e. for 766,370 is 141710.

Thus, GCF of Fractions is 2/141710.Finally, GCF of Fractions for 738/766, 7688/370 is 2/141710.