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GCF of 281/52, 217/540

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 281/52, 217/540 i.e 1/7020 easily. The following is the detailed procedure to determine the greatest common factor of fractions 281/52, 217/540.

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 281/52,217/540?

Given fractions are 281/52,217/540

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 281/52,217/540, numerators are 281,217

Denominators are 52,540

The GCF of 281,217 is 1 .

LCM of 52,540 is 7020.

The greatest common factor of 281/52,217/540 = [GCF of 281,217]/[LCM of 52,540]= 1/7020

Therefore, the GCF of 281/52,217/540 is 1/7020.

Greatest Common Factor of 281,217

To find the highest common factor of 281,217, we have to find the factors of both numbers and list the highest common factor.

The factors of 281 are 1, 281

The factors of 217 are 1, 7, 31, 217

The HCF of 281,217 is 1.

Lets's calculate GCF of 281,217

Greatest Common Factor (GCF) of 281,217 By Common Division

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

Greatest Common Factor of 281,217 By Matching Biggest Common Factor Method

Greatest Common Factor of 281,217 By Matching Biggest Common Factor Method

Now, list down the factors of 281

:

1,281

Now, list down the factors of 217

:

1,7,31,217

Greatest Common Factor

We found the factors 281,217 . The biggest common factor number is the GCF number.
So the greatest common factor 281,217 is 1.

Lets's calculate LCM of 52,540

Lowest Common Multiple of 52,540 using Common Division

2 52, 540
2 26, 270
13, 135

∴ So the LCM of the given numbers is 2 x 2 x 13 x 135 = 7020

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7020

Therefore, the GCF of Fractions 281/52,217/540 is 1/7020

Least Common Multiple of 52,540 with GCF Formula

Least Common Multiple of 52,540 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 52,540 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(52,540) = 4

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

GCF(52,540) x common factors =4 x 1 = 4

LCM(52,540) = ( 52 × 540 ) / 4

LCM(52,540) = 28080 / 4

LCM(52,540) = 7020


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FAQs on GCF of Fractions of 281/52, 217/540

1. What is the HCF of 281,217?

The HCF of 281,217 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 281/52, 217/540?

Answer: GCF of Numerators as per given numbers 281/52, 217/540 is

GCF of Numerators i.e. for 281,217 is 1

LCM of denominators i.e. for 52,540 is 7020.

Thus, GCF of Fractions is 1/7020.Finally, GCF of Fractions for 281/52, 217/540 is 1/7020.