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GCF of 729/20, 652/778

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 729/20, 652/778 i.e 1/7780 easily. The following is the detailed procedure to determine the greatest common factor of fractions 729/20, 652/778.

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 729/20,652/778?

Given fractions are 729/20,652/778

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 729/20,652/778, numerators are 729,652

Denominators are 20,778

The GCF of 729,652 is 1 .

LCM of 20,778 is 7780.

The greatest common factor of 729/20,652/778 = [GCF of 729,652]/[LCM of 20,778]= 1/7780

Therefore, the GCF of 729/20,652/778 is 1/7780.

Greatest Common Factor of 729,652

To find the highest common factor of 729,652, we have to find the factors of both numbers and list the highest common factor.

The factors of 729 are 1, 3, 9, 27, 81, 243, 729

The factors of 652 are 1, 2, 4, 163, 326, 652

The HCF of 729,652 is 1.

Lets's calculate GCF of 729,652

Greatest Common Factor (GCF) of 729,652 By Common Division

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

Greatest Common Factor of 729,652 By Matching Biggest Common Factor Method

Greatest Common Factor of 729,652 By Matching Biggest Common Factor Method

Now, list down the factors of 729

:

1,3,9,27,81,243,729

Now, list down the factors of 652

:

1,2,4,163,326,652

Greatest Common Factor

We found the factors 729,652 . The biggest common factor number is the GCF number.
So the greatest common factor 729,652 is 1.

Lets's calculate LCM of 20,778

Lowest Common Multiple of 20,778 using Common Division

2 20, 778
10, 389

∴ So the LCM of the given numbers is 2 x 10 x 389 = 7780

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/7780

Therefore, the GCF of Fractions 729/20,652/778 is 1/7780

Least Common Multiple of 20,778 with GCF Formula

Least Common Multiple of 20,778 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 20,778 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(20,778) = 2

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

GCF(20,778) x common factors =2 x 1 = 2

LCM(20,778) = ( 20 × 778 ) / 2

LCM(20,778) = 15560 / 2

LCM(20,778) = 7780


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FAQs on GCF of Fractions of 729/20, 652/778

1. What is the HCF of 729,652?

The HCF of 729,652 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 729/20, 652/778?

Answer: GCF of Numerators as per given numbers 729/20, 652/778 is

GCF of Numerators i.e. for 729,652 is 1

LCM of denominators i.e. for 20,778 is 7780.

Thus, GCF of Fractions is 1/7780.Finally, GCF of Fractions for 729/20, 652/778 is 1/7780.