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GCF of 305/67, 255/140

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 305/67, 255/140 i.e 5/9380 easily. The following is the detailed procedure to determine the greatest common factor of fractions 305/67, 255/140.

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 305/67,255/140?

Given fractions are 305/67,255/140

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 305/67,255/140, numerators are 305,255

Denominators are 67,140

The GCF of 305,255 is 5 .

LCM of 67,140 is 9380.

The greatest common factor of 305/67,255/140 = [GCF of 305,255]/[LCM of 67,140]= 5/9380

Therefore, the GCF of 305/67,255/140 is 5/9380.

Greatest Common Factor of 305,255

To find the highest common factor of 305,255, we have to find the factors of both numbers and list the highest common factor.

The factors of 305 are 1, 5, 61, 305

The factors of 255 are 1, 3, 5, 15, 17, 51, 85, 255

The HCF of 305,255 is 5.

Lets's calculate GCF of 305,255

Greatest Common Factor (GCF) of 305,255 By Common Division

5 305, 255
61, 51

∴ So the GCF of the given numbers is 5 = 5

Greatest Common Factor of 305,255 By Matching Biggest Common Factor Method

Greatest Common Factor of 305,255 By Matching Biggest Common Factor Method

Now, list down the factors of 305

:

1,5,61,305

Now, list down the factors of 255

:

1,3,5,15,17,51,85,255

Greatest Common Factor

We found the factors 305,255 . The biggest common factor number is the GCF number.
So the greatest common factor 305,255 is 5.

Lets's calculate LCM of 67,140

Lowest Common Multiple of 67,140 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 9380

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/9380

Therefore, the GCF of Fractions 305/67,255/140 is 5/9380

Least Common Multiple of 67,140 with GCF Formula

Least Common Multiple of 67,140 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 67,140 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(67,140) = 1

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

GCF(67,140) x common factors =1 x 1 = 1

LCM(67,140) = ( 67 × 140 ) / 1

LCM(67,140) = 9380 / 1

LCM(67,140) = 9380


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FAQs on GCF of Fractions of 305/67, 255/140

1. What is the HCF of 305,255?

The HCF of 305,255 is 5

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 305/67, 255/140?

Answer: GCF of Numerators as per given numbers 305/67, 255/140 is

GCF of Numerators i.e. for 305,255 is 5

LCM of denominators i.e. for 67,140 is 9380.

Thus, GCF of Fractions is 5/9380.Finally, GCF of Fractions for 305/67, 255/140 is 5/9380.