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GCF of 13/310, 271/154

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 13/310, 271/154 i.e 1/23870 easily. The following is the detailed procedure to determine the greatest common factor of fractions 13/310, 271/154.

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 13/310,271/154?

Given fractions are 13/310,271/154

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 13/310,271/154, numerators are 13,271

Denominators are 310,154

The GCF of 13,271 is 1 .

LCM of 310,154 is 23870.

The greatest common factor of 13/310,271/154 = [GCF of 13,271]/[LCM of 310,154]= 1/23870

Therefore, the GCF of 13/310,271/154 is 1/23870.

Greatest Common Factor of 13,271

To find the highest common factor of 13,271, we have to find the factors of both numbers and list the highest common factor.

The factors of 13 are 1, 13

The factors of 271 are 1, 271

The HCF of 13,271 is 1.

Lets's calculate GCF of 13,271

Greatest Common Factor (GCF) of 13,271 By Common Division

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

Greatest Common Factor of 13,271 By Matching Biggest Common Factor Method

Greatest Common Factor of 13,271 By Matching Biggest Common Factor Method

Now, list down the factors of 13

:

1,13

Now, list down the factors of 271

:

1,271

Greatest Common Factor

We found the factors 13,271 . The biggest common factor number is the GCF number.
So the greatest common factor 13,271 is 1.

Lets's calculate LCM of 310,154

Lowest Common Multiple of 310,154 using Common Division

2 310, 154
155, 77

∴ So the LCM of the given numbers is 2 x 155 x 77 = 23870

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/23870

Therefore, the GCF of Fractions 13/310,271/154 is 1/23870

Least Common Multiple of 310,154 with GCF Formula

Least Common Multiple of 310,154 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 310,154 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(310,154) = 2

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

GCF(310,154) x common factors =2 x 1 = 2

LCM(310,154) = ( 310 × 154 ) / 2

LCM(310,154) = 47740 / 2

LCM(310,154) = 23870


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FAQs on GCF of Fractions of 13/310, 271/154

1. What is the HCF of 13,271?

The HCF of 13,271 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 13/310, 271/154?

Answer: GCF of Numerators as per given numbers 13/310, 271/154 is

GCF of Numerators i.e. for 13,271 is 1

LCM of denominators i.e. for 310,154 is 23870.

Thus, GCF of Fractions is 1/23870.Finally, GCF of Fractions for 13/310, 271/154 is 1/23870.