How to Find GCF of 123/728, 1382/978?

GCF of 123/728, 1382/978

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 123/728, 1382/978 i.e 1/355992 easily. The following is the detailed procedure to determine the greatest common factor of fractions 123/728, 1382/978.

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 123/728,1382/978?

Given fractions are 123/728,1382/978

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 123/728,1382/978, numerators are 123,1382

Denominators are 728,978

The GCF of 123,1382 is 1 .

LCM of 728,978 is 355992.

The greatest common factor of 123/728,1382/978 = [GCF of 123,1382]/[LCM of 728,978]= 1/355992

Therefore, the GCF of 123/728,1382/978 is 1/355992.

Greatest Common Factor of 123,1382

To find the highest common factor of 123,1382, we have to find the factors of both numbers and list the highest common factor.

The factors of 123 are 1, 3, 41, 123

The factors of 1382 are 1, 2, 691, 1382

The HCF of 123,1382 is 1.

Lets's calculate GCF of 123,1382

Greatest Common Factor (GCF) of 123,1382 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 123,1382 By Matching Biggest Common Factor Method

Now, list down the factors of 123

1,3,41,123

Now, list down the factors of 1382

1,2,691,1382

Greatest Common Factor

We found the factors 123,1382 . The biggest common factor number is the GCF number.
So the greatest common factor 123,1382 is 1.

Lets's calculate LCM of 728,978

Lowest Common Multiple of 728,978 using Common Division

2	728, 978
	364, 489

∴ So the LCM of the given numbers is 2 x 364 x 489 = 355992

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/355992

Therefore, the GCF of Fractions 123/728,1382/978 is 1/355992

Least Common Multiple of 728,978 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 728,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(728,978) = 2

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

GCF(728,978) x common factors =2 x 1 = 2

LCM(728,978) = ( 728 × 978 ) / 2

LCM(728,978) = 711984 / 2

LCM(728,978) = 355992

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 123/728, 1382/978

1. What is the HCF of 123,1382?

The HCF of 123,1382 is 1

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 123/728, 1382/978?

Answer: GCF of Numerators as per given numbers 123/728, 1382/978 is

GCF of Numerators i.e. for 123,1382 is 1

LCM of denominators i.e. for 728,978 is 355992.

Thus, GCF of Fractions is 1/355992.Finally, GCF of Fractions for 123/728, 1382/978 is 1/355992.