How to Find GCF of 130/31, 360/256?

GCF of 130/31, 360/256

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 130/31, 360/256 i.e 10/7936 easily. The following is the detailed procedure to determine the greatest common factor of fractions 130/31, 360/256.

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 130/31,360/256?

Given fractions are 130/31,360/256

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 130/31,360/256, numerators are 130,360

Denominators are 31,256

The GCF of 130,360 is 10 .

LCM of 31,256 is 7936.

The greatest common factor of 130/31,360/256 = [GCF of 130,360]/[LCM of 31,256]= 10/7936

Therefore, the GCF of 130/31,360/256 is 10/7936.

Greatest Common Factor of 130,360

To find the highest common factor of 130,360, we have to find the factors of both numbers and list the highest common factor.

The factors of 130 are 1, 2, 5, 10, 13, 26, 65, 130

The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360

The HCF of 130,360 is 10.

Lets's calculate GCF of 130,360

Greatest Common Factor (GCF) of 130,360 By Common Division

2	130, 360
5	65, 180
	13, 36

∴ So the GCF of the given numbers is 2 x 5 = 10

Greatest Common Factor of 130,360 By Matching Biggest Common Factor Method

Now, list down the factors of 130

1,2,5,10,13,26,65,130

Now, list down the factors of 360

1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180,360

Greatest Common Factor

We found the factors 130,360 . The biggest common factor number is the GCF number.
So the greatest common factor 130,360 is 10.

Lets's calculate LCM of 31,256

Lowest Common Multiple of 31,256 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 7936

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/7936

Therefore, the GCF of Fractions 130/31,360/256 is 10/7936

Least Common Multiple of 31,256 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 31,256 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,256) = 1

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

GCF(31,256) x common factors =1 x 1 = 1

LCM(31,256) = ( 31 × 256 ) / 1

LCM(31,256) = 7936 / 1

LCM(31,256) = 7936

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FAQs on GCF of Fractions of 130/31, 360/256

1. What is the HCF of 130,360?

The HCF of 130,360 is 10

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 130/31, 360/256?

Answer: GCF of Numerators as per given numbers 130/31, 360/256 is

GCF of Numerators i.e. for 130,360 is 10

LCM of denominators i.e. for 31,256 is 7936.

Thus, GCF of Fractions is 10/7936.Finally, GCF of Fractions for 130/31, 360/256 is 10/7936.