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GCF of 321/508, 765/509

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 321/508, 765/509 i.e 3/258572 easily. The following is the detailed procedure to determine the greatest common factor of fractions 321/508, 765/509.

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 321/508,765/509?

Given fractions are 321/508,765/509

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 321/508,765/509, numerators are 321,765

Denominators are 508,509

The GCF of 321,765 is 3 .

LCM of 508,509 is 258572.

The greatest common factor of 321/508,765/509 = [GCF of 321,765]/[LCM of 508,509]= 3/258572

Therefore, the GCF of 321/508,765/509 is 3/258572.

Greatest Common Factor of 321,765

To find the highest common factor of 321,765, we have to find the factors of both numbers and list the highest common factor.

The factors of 321 are 1, 3, 107, 321

The factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765

The HCF of 321,765 is 3.

Lets's calculate GCF of 321,765

Greatest Common Factor (GCF) of 321,765 By Common Division

3 321, 765
107, 255

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

Greatest Common Factor of 321,765 By Matching Biggest Common Factor Method

Greatest Common Factor of 321,765 By Matching Biggest Common Factor Method

Now, list down the factors of 321

:

1,3,107,321

Now, list down the factors of 765

:

1,3,5,9,15,17,45,51,85,153,255,765

Greatest Common Factor

We found the factors 321,765 . The biggest common factor number is the GCF number.
So the greatest common factor 321,765 is 3.

Lets's calculate LCM of 508,509

Lowest Common Multiple of 508,509 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 258572

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/258572

Therefore, the GCF of Fractions 321/508,765/509 is 3/258572

Least Common Multiple of 508,509 with GCF Formula

Least Common Multiple of 508,509 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 508,509 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(508,509) = 1

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

GCF(508,509) x common factors =1 x 1 = 1

LCM(508,509) = ( 508 × 509 ) / 1

LCM(508,509) = 258572 / 1

LCM(508,509) = 258572


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FAQs on GCF of Fractions of 321/508, 765/509

1. What is the HCF of 321,765?

The HCF of 321,765 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 321/508, 765/509?

Answer: GCF of Numerators as per given numbers 321/508, 765/509 is

GCF of Numerators i.e. for 321,765 is 3

LCM of denominators i.e. for 508,509 is 258572.

Thus, GCF of Fractions is 3/258572.Finally, GCF of Fractions for 321/508, 765/509 is 3/258572.