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GCF of 802/683, 214/829

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 802/683, 214/829 i.e 2/566207 easily. The following is the detailed procedure to determine the greatest common factor of fractions 802/683, 214/829.

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 802/683,214/829?

Given fractions are 802/683,214/829

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 802/683,214/829, numerators are 802,214

Denominators are 683,829

The GCF of 802,214 is 2 .

LCM of 683,829 is 566207.

The greatest common factor of 802/683,214/829 = [GCF of 802,214]/[LCM of 683,829]= 2/566207

Therefore, the GCF of 802/683,214/829 is 2/566207.

Greatest Common Factor of 802,214

To find the highest common factor of 802,214, 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 214 are 1, 2, 107, 214

The HCF of 802,214 is 2.

Lets's calculate GCF of 802,214

Greatest Common Factor (GCF) of 802,214 By Common Division

2 802, 214
401, 107

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

Greatest Common Factor of 802,214 By Matching Biggest Common Factor Method

Greatest Common Factor of 802,214 By Matching Biggest Common Factor Method

Now, list down the factors of 802

:

1,2,401,802

Now, list down the factors of 214

:

1,2,107,214

Greatest Common Factor

We found the factors 802,214 . The biggest common factor number is the GCF number.
So the greatest common factor 802,214 is 2.

Lets's calculate LCM of 683,829

Lowest Common Multiple of 683,829 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 566207

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/566207

Therefore, the GCF of Fractions 802/683,214/829 is 2/566207

Least Common Multiple of 683,829 with GCF Formula

Least Common Multiple of 683,829 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 683,829 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(683,829) = 1

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

GCF(683,829) x common factors =1 x 1 = 1

LCM(683,829) = ( 683 × 829 ) / 1

LCM(683,829) = 566207 / 1

LCM(683,829) = 566207


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FAQs on GCF of Fractions of 802/683, 214/829

1. What is the HCF of 802,214?

The HCF of 802,214 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 802/683, 214/829?

Answer: GCF of Numerators as per given numbers 802/683, 214/829 is

GCF of Numerators i.e. for 802,214 is 2

LCM of denominators i.e. for 683,829 is 566207.

Thus, GCF of Fractions is 2/566207.Finally, GCF of Fractions for 802/683, 214/829 is 2/566207.