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GCF of 231/23, 540/151

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 231/23, 540/151 i.e 3/3473 easily. The following is the detailed procedure to determine the greatest common factor of fractions 231/23, 540/151.

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 231/23,540/151?

Given fractions are 231/23,540/151

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 231/23,540/151, numerators are 231,540

Denominators are 23,151

The GCF of 231,540 is 3 .

LCM of 23,151 is 3473.

The greatest common factor of 231/23,540/151 = [GCF of 231,540]/[LCM of 23,151]= 3/3473

Therefore, the GCF of 231/23,540/151 is 3/3473.

Greatest Common Factor of 231,540

To find the highest common factor of 231,540, we have to find the factors of both numbers and list the highest common factor.

The factors of 231 are 1, 3, 7, 11, 21, 33, 77, 231

The factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540

The HCF of 231,540 is 3.

Lets's calculate GCF of 231,540

Greatest Common Factor (GCF) of 231,540 By Common Division

3 231, 540
77, 180

∴ So the GCF of the given numbers is 3 = 3

Greatest Common Factor of 231,540 By Matching Biggest Common Factor Method

Greatest Common Factor of 231,540 By Matching Biggest Common Factor Method

Now, list down the factors of 231

:

1,3,7,11,21,33,77,231

Now, list down the factors of 540

:

1,2,3,4,5,6,9,10,12,15,18,20,27,30,36,45,54,60,90,108,135,180,270,540

Greatest Common Factor

We found the factors 231,540 . The biggest common factor number is the GCF number.
So the greatest common factor 231,540 is 3.

Lets's calculate LCM of 23,151

Lowest Common Multiple of 23,151 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 3473

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/3473

Therefore, the GCF of Fractions 231/23,540/151 is 3/3473

Least Common Multiple of 23,151 with GCF Formula

Least Common Multiple of 23,151 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 23,151 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(23,151) = 1

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

GCF(23,151) x common factors =1 x 1 = 1

LCM(23,151) = ( 23 × 151 ) / 1

LCM(23,151) = 3473 / 1

LCM(23,151) = 3473


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FAQs on GCF of Fractions of 231/23, 540/151

1. What is the HCF of 231,540?

The HCF of 231,540 is 3

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 231/23, 540/151?

Answer: GCF of Numerators as per given numbers 231/23, 540/151 is

GCF of Numerators i.e. for 231,540 is 3

LCM of denominators i.e. for 23,151 is 3473.

Thus, GCF of Fractions is 3/3473.Finally, GCF of Fractions for 231/23, 540/151 is 3/3473.