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GCF of 729/402, 397/210

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 729/402, 397/210 i.e 1/14070 easily. The following is the detailed procedure to determine the greatest common factor of fractions 729/402, 397/210.

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 729/402,397/210?

Given fractions are 729/402,397/210

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 729/402,397/210, numerators are 729,397

Denominators are 402,210

The GCF of 729,397 is 1 .

LCM of 402,210 is 14070.

The greatest common factor of 729/402,397/210 = [GCF of 729,397]/[LCM of 402,210]= 1/14070

Therefore, the GCF of 729/402,397/210 is 1/14070.

Greatest Common Factor of 729,397

To find the highest common factor of 729,397, 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 397 are 1, 397

The HCF of 729,397 is 1.

Lets's calculate GCF of 729,397

Greatest Common Factor (GCF) of 729,397 By Common Division

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

Greatest Common Factor of 729,397 By Matching Biggest Common Factor Method

Greatest Common Factor of 729,397 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 397

:

1,397

Greatest Common Factor

We found the factors 729,397 . The biggest common factor number is the GCF number.
So the greatest common factor 729,397 is 1.

Lets's calculate LCM of 402,210

Lowest Common Multiple of 402,210 using Common Division

2 402, 210
3 201, 105
67, 35

∴ So the LCM of the given numbers is 2 x 3 x 67 x 35 = 14070

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/14070

Therefore, the GCF of Fractions 729/402,397/210 is 1/14070

Least Common Multiple of 402,210 with GCF Formula

Least Common Multiple of 402,210 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 402,210 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(402,210) = 6

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

GCF(402,210) x common factors =6 x 1 = 6

LCM(402,210) = ( 402 × 210 ) / 6

LCM(402,210) = 84420 / 6

LCM(402,210) = 14070


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FAQs on GCF of Fractions of 729/402, 397/210

1. What is the HCF of 729,397?

The HCF of 729,397 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 729/402, 397/210?

Answer: GCF of Numerators as per given numbers 729/402, 397/210 is

GCF of Numerators i.e. for 729,397 is 1

LCM of denominators i.e. for 402,210 is 14070.

Thus, GCF of Fractions is 1/14070.Finally, GCF of Fractions for 729/402, 397/210 is 1/14070.