How to Find GCF of 572/760, 7709/509?

GCF of 572/760, 7709/509

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 572/760, 7709/509 i.e 13/386840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 572/760, 7709/509.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 572/760,7709/509?

Given fractions are 572/760,7709/509

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 572/760,7709/509, numerators are 572,7709

Denominators are 760,509

The GCF of 572,7709 is 13 .

LCM of 760,509 is 386840.

The greatest common factor of 572/760,7709/509 = [GCF of 572,7709]/[LCM of 760,509]= 13/386840

Therefore, the GCF of 572/760,7709/509 is 13/386840.

Greatest Common Factor of 572,7709

To find the highest common factor of 572,7709, we have to find the factors of both numbers and list the highest common factor.

The factors of 572 are 1, 2, 4, 11, 13, 22, 26, 44, 52, 143, 286, 572

The factors of 7709 are 1, 13, 593, 7709

The HCF of 572,7709 is 13.

Lets's calculate GCF of 572,7709

Greatest Common Factor (GCF) of 572,7709 By Common Division

13	572, 7709
	44, 593

∴ So the GCF of the given numbers is 13 = 13

Greatest Common Factor of 572,7709 By Matching Biggest Common Factor Method

Now, list down the factors of 572

1,2,4,11,13,22,26,44,52,143,286,572

Now, list down the factors of 7709

1,13,593,7709

Greatest Common Factor

We found the factors 572,7709 . The biggest common factor number is the GCF number.
So the greatest common factor 572,7709 is 13.

Lets's calculate LCM of 760,509

Lowest Common Multiple of 760,509 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 386840

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 13/386840

Therefore, the GCF of Fractions 572/760,7709/509 is 13/386840

Least Common Multiple of 760,509 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 760,509 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(760,509) = 1

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

GCF(760,509) x common factors =1 x 1 = 1

LCM(760,509) = ( 760 × 509 ) / 1

LCM(760,509) = 386840 / 1

LCM(760,509) = 386840

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FAQs on GCF of Fractions of 572/760, 7709/509

1. What is the HCF of 572,7709?

The HCF of 572,7709 is 13

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 572/760, 7709/509?

Answer: GCF of Numerators as per given numbers 572/760, 7709/509 is

GCF of Numerators i.e. for 572,7709 is 13

LCM of denominators i.e. for 760,509 is 386840.

Thus, GCF of Fractions is 13/386840.Finally, GCF of Fractions for 572/760, 7709/509 is 13/386840.