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GCF of 140/17, 506/310

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 140/17, 506/310 i.e 2/5270 easily. The following is the detailed procedure to determine the greatest common factor of fractions 140/17, 506/310.

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 140/17,506/310?

Given fractions are 140/17,506/310

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 140/17,506/310, numerators are 140,506

Denominators are 17,310

The GCF of 140,506 is 2 .

LCM of 17,310 is 5270.

The greatest common factor of 140/17,506/310 = [GCF of 140,506]/[LCM of 17,310]= 2/5270

Therefore, the GCF of 140/17,506/310 is 2/5270.

Greatest Common Factor of 140,506

To find the highest common factor of 140,506, we have to find the factors of both numbers and list the highest common factor.

The factors of 140 are 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140

The factors of 506 are 1, 2, 11, 22, 23, 46, 253, 506

The HCF of 140,506 is 2.

Lets's calculate GCF of 140,506

Greatest Common Factor (GCF) of 140,506 By Common Division

2 140, 506
70, 253

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

Greatest Common Factor of 140,506 By Matching Biggest Common Factor Method

Greatest Common Factor of 140,506 By Matching Biggest Common Factor Method

Now, list down the factors of 140

:

1,2,4,5,7,10,14,20,28,35,70,140

Now, list down the factors of 506

:

1,2,11,22,23,46,253,506

Greatest Common Factor

We found the factors 140,506 . The biggest common factor number is the GCF number.
So the greatest common factor 140,506 is 2.

Lets's calculate LCM of 17,310

Lowest Common Multiple of 17,310 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 5270

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/5270

Therefore, the GCF of Fractions 140/17,506/310 is 2/5270

Least Common Multiple of 17,310 with GCF Formula

Least Common Multiple of 17,310 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 17,310 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(17,310) = 1

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

GCF(17,310) x common factors =1 x 1 = 1

LCM(17,310) = ( 17 × 310 ) / 1

LCM(17,310) = 5270 / 1

LCM(17,310) = 5270


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FAQs on GCF of Fractions of 140/17, 506/310

1. What is the HCF of 140,506?

The HCF of 140,506 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 140/17, 506/310?

Answer: GCF of Numerators as per given numbers 140/17, 506/310 is

GCF of Numerators i.e. for 140,506 is 2

LCM of denominators i.e. for 17,310 is 5270.

Thus, GCF of Fractions is 2/5270.Finally, GCF of Fractions for 140/17, 506/310 is 2/5270.