How to Find GCF of 700/131, 978/413?

GCF of 700/131, 978/413

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 700/131, 978/413 i.e 2/54103 easily. The following is the detailed procedure to determine the greatest common factor of fractions 700/131, 978/413.

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 700/131,978/413?

Given fractions are 700/131,978/413

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 700/131,978/413, numerators are 700,978

Denominators are 131,413

The GCF of 700,978 is 2 .

LCM of 131,413 is 54103.

The greatest common factor of 700/131,978/413 = [GCF of 700,978]/[LCM of 131,413]= 2/54103

Therefore, the GCF of 700/131,978/413 is 2/54103.

Greatest Common Factor of 700,978

To find the highest common factor of 700,978, we have to find the factors of both numbers and list the highest common factor.

The factors of 700 are 1, 2, 4, 5, 7, 10, 14, 20, 25, 28, 35, 50, 70, 100, 140, 175, 350, 700

The factors of 978 are 1, 2, 3, 6, 163, 326, 489, 978

The HCF of 700,978 is 2.

Lets's calculate GCF of 700,978

Greatest Common Factor (GCF) of 700,978 By Common Division

2	700, 978
	350, 489

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

Greatest Common Factor of 700,978 By Matching Biggest Common Factor Method

Now, list down the factors of 700

1,2,4,5,7,10,14,20,25,28,35,50,70,100,140,175,350,700

Now, list down the factors of 978

1,2,3,6,163,326,489,978

Greatest Common Factor

We found the factors 700,978 . The biggest common factor number is the GCF number.
So the greatest common factor 700,978 is 2.

Lets's calculate LCM of 131,413

Lowest Common Multiple of 131,413 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 54103

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/54103

Therefore, the GCF of Fractions 700/131,978/413 is 2/54103

Least Common Multiple of 131,413 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 131,413 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(131,413) = 1

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

GCF(131,413) x common factors =1 x 1 = 1

LCM(131,413) = ( 131 × 413 ) / 1

LCM(131,413) = 54103 / 1

LCM(131,413) = 54103

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 700/131, 978/413

1. What is the HCF of 700,978?

The HCF of 700,978 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 700/131, 978/413?

Answer: GCF of Numerators as per given numbers 700/131, 978/413 is

GCF of Numerators i.e. for 700,978 is 2

LCM of denominators i.e. for 131,413 is 54103.

Thus, GCF of Fractions is 2/54103.Finally, GCF of Fractions for 700/131, 978/413 is 2/54103.