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GCF of 232/65, 721/6214

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 232/65, 721/6214 i.e 1/31070 easily. The following is the detailed procedure to determine the greatest common factor of fractions 232/65, 721/6214.

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 232/65,721/6214?

Given fractions are 232/65,721/6214

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 232/65,721/6214, numerators are 232,721

Denominators are 65,6214

The GCF of 232,721 is 1 .

LCM of 65,6214 is 31070.

The greatest common factor of 232/65,721/6214 = [GCF of 232,721]/[LCM of 65,6214]= 1/31070

Therefore, the GCF of 232/65,721/6214 is 1/31070.

Greatest Common Factor of 232,721

To find the highest common factor of 232,721, we have to find the factors of both numbers and list the highest common factor.

The factors of 232 are 1, 2, 4, 8, 29, 58, 116, 232

The factors of 721 are 1, 7, 103, 721

The HCF of 232,721 is 1.

Lets's calculate GCF of 232,721

Greatest Common Factor (GCF) of 232,721 By Common Division

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

Greatest Common Factor of 232,721 By Matching Biggest Common Factor Method

Greatest Common Factor of 232,721 By Matching Biggest Common Factor Method

Now, list down the factors of 232

:

1,2,4,8,29,58,116,232

Now, list down the factors of 721

:

1,7,103,721

Greatest Common Factor

We found the factors 232,721 . The biggest common factor number is the GCF number.
So the greatest common factor 232,721 is 1.

Lets's calculate LCM of 65,6214

Lowest Common Multiple of 65,6214 using Common Division

13 65, 6214
5, 478

∴ So the LCM of the given numbers is 13 x 5 x 478 = 31070

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/31070

Therefore, the GCF of Fractions 232/65,721/6214 is 1/31070

Least Common Multiple of 65,6214 with GCF Formula

Least Common Multiple of 65,6214 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 65,6214 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(65,6214) = 13

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

GCF(65,6214) x common factors =13 x 1 = 13

LCM(65,6214) = ( 65 × 6214 ) / 13

LCM(65,6214) = 403910 / 13

LCM(65,6214) = 31070


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FAQs on GCF of Fractions of 232/65, 721/6214

1. What is the HCF of 232,721?

The HCF of 232,721 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 232/65, 721/6214?

Answer: GCF of Numerators as per given numbers 232/65, 721/6214 is

GCF of Numerators i.e. for 232,721 is 1

LCM of denominators i.e. for 65,6214 is 31070.

Thus, GCF of Fractions is 1/31070.Finally, GCF of Fractions for 232/65, 721/6214 is 1/31070.