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GCF of 282/34, 731/562

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 282/34, 731/562 i.e 1/9554 easily. The following is the detailed procedure to determine the greatest common factor of fractions 282/34, 731/562.

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 282/34,731/562?

Given fractions are 282/34,731/562

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 282/34,731/562, numerators are 282,731

Denominators are 34,562

The GCF of 282,731 is 1 .

LCM of 34,562 is 9554.

The greatest common factor of 282/34,731/562 = [GCF of 282,731]/[LCM of 34,562]= 1/9554

Therefore, the GCF of 282/34,731/562 is 1/9554.

Greatest Common Factor of 282,731

To find the highest common factor of 282,731, we have to find the factors of both numbers and list the highest common factor.

The factors of 282 are 1, 2, 3, 6, 47, 94, 141, 282

The factors of 731 are 1, 17, 43, 731

The HCF of 282,731 is 1.

Lets's calculate GCF of 282,731

Greatest Common Factor (GCF) of 282,731 By Common Division

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

Greatest Common Factor of 282,731 By Matching Biggest Common Factor Method

Greatest Common Factor of 282,731 By Matching Biggest Common Factor Method

Now, list down the factors of 282

:

1,2,3,6,47,94,141,282

Now, list down the factors of 731

:

1,17,43,731

Greatest Common Factor

We found the factors 282,731 . The biggest common factor number is the GCF number.
So the greatest common factor 282,731 is 1.

Lets's calculate LCM of 34,562

Lowest Common Multiple of 34,562 using Common Division

2 34, 562
17, 281

∴ So the LCM of the given numbers is 2 x 17 x 281 = 9554

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/9554

Therefore, the GCF of Fractions 282/34,731/562 is 1/9554

Least Common Multiple of 34,562 with GCF Formula

Least Common Multiple of 34,562 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 34,562 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(34,562) = 2

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

GCF(34,562) x common factors =2 x 1 = 2

LCM(34,562) = ( 34 × 562 ) / 2

LCM(34,562) = 19108 / 2

LCM(34,562) = 9554


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FAQs on GCF of Fractions of 282/34, 731/562

1. What is the HCF of 282,731?

The HCF of 282,731 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 282/34, 731/562?

Answer: GCF of Numerators as per given numbers 282/34, 731/562 is

GCF of Numerators i.e. for 282,731 is 1

LCM of denominators i.e. for 34,562 is 9554.

Thus, GCF of Fractions is 1/9554.Finally, GCF of Fractions for 282/34, 731/562 is 1/9554.