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GCF of 802/12, 824/289

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 802/12, 824/289 i.e 2/3468 easily. The following is the detailed procedure to determine the greatest common factor of fractions 802/12, 824/289.

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 802/12,824/289?

Given fractions are 802/12,824/289

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 802/12,824/289, numerators are 802,824

Denominators are 12,289

The GCF of 802,824 is 2 .

LCM of 12,289 is 3468.

The greatest common factor of 802/12,824/289 = [GCF of 802,824]/[LCM of 12,289]= 2/3468

Therefore, the GCF of 802/12,824/289 is 2/3468.

Greatest Common Factor of 802,824

To find the highest common factor of 802,824, we have to find the factors of both numbers and list the highest common factor.

The factors of 802 are 1, 2, 401, 802

The factors of 824 are 1, 2, 4, 8, 103, 206, 412, 824

The HCF of 802,824 is 2.

Lets's calculate GCF of 802,824

Greatest Common Factor (GCF) of 802,824 By Common Division

2 802, 824
401, 412

∴ So the GCF of the given numbers is 2 = 2

Greatest Common Factor of 802,824 By Matching Biggest Common Factor Method

Greatest Common Factor of 802,824 By Matching Biggest Common Factor Method

Now, list down the factors of 802

:

1,2,401,802

Now, list down the factors of 824

:

1,2,4,8,103,206,412,824

Greatest Common Factor

We found the factors 802,824 . The biggest common factor number is the GCF number.
So the greatest common factor 802,824 is 2.

Lets's calculate LCM of 12,289

Lowest Common Multiple of 12,289 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 3468

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/3468

Therefore, the GCF of Fractions 802/12,824/289 is 2/3468

Least Common Multiple of 12,289 with GCF Formula

Least Common Multiple of 12,289 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 12,289 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(12,289) = 1

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

GCF(12,289) x common factors =1 x 1 = 1

LCM(12,289) = ( 12 × 289 ) / 1

LCM(12,289) = 3468 / 1

LCM(12,289) = 3468


GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 802/12, 824/289

1. What is the HCF of 802,824?

The HCF of 802,824 is 2

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 802/12, 824/289?

Answer: GCF of Numerators as per given numbers 802/12, 824/289 is

GCF of Numerators i.e. for 802,824 is 2

LCM of denominators i.e. for 12,289 is 3468.

Thus, GCF of Fractions is 2/3468.Finally, GCF of Fractions for 802/12, 824/289 is 2/3468.