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GCF of 682/704, 286/307

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 682/704, 286/307 i.e 22/216128 easily. The following is the detailed procedure to determine the greatest common factor of fractions 682/704, 286/307.

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 682/704,286/307?

Given fractions are 682/704,286/307

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 682/704,286/307, numerators are 682,286

Denominators are 704,307

The GCF of 682,286 is 22 .

LCM of 704,307 is 216128.

The greatest common factor of 682/704,286/307 = [GCF of 682,286]/[LCM of 704,307]= 22/216128

Therefore, the GCF of 682/704,286/307 is 22/216128.

Greatest Common Factor of 682,286

To find the highest common factor of 682,286, we have to find the factors of both numbers and list the highest common factor.

The factors of 682 are 1, 2, 11, 22, 31, 62, 341, 682

The factors of 286 are 1, 2, 11, 13, 22, 26, 143, 286

The HCF of 682,286 is 22.

Lets's calculate GCF of 682,286

Greatest Common Factor (GCF) of 682,286 By Common Division

2 682, 286
11 341, 143
31, 13

∴ So the GCF of the given numbers is 2 x 11 = 22

Greatest Common Factor of 682,286 By Matching Biggest Common Factor Method

Greatest Common Factor of 682,286 By Matching Biggest Common Factor Method

Now, list down the factors of 682

:

1,2,11,22,31,62,341,682

Now, list down the factors of 286

:

1,2,11,13,22,26,143,286

Greatest Common Factor

We found the factors 682,286 . The biggest common factor number is the GCF number.
So the greatest common factor 682,286 is 22.

Lets's calculate LCM of 704,307

Lowest Common Multiple of 704,307 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 216128

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 22/216128

Therefore, the GCF of Fractions 682/704,286/307 is 22/216128

Least Common Multiple of 704,307 with GCF Formula

Least Common Multiple of 704,307 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 704,307 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(704,307) = 1

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

GCF(704,307) x common factors =1 x 1 = 1

LCM(704,307) = ( 704 × 307 ) / 1

LCM(704,307) = 216128 / 1

LCM(704,307) = 216128


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FAQs on GCF of Fractions of 682/704, 286/307

1. What is the HCF of 682,286?

The HCF of 682,286 is 22

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 682/704, 286/307?

Answer: GCF of Numerators as per given numbers 682/704, 286/307 is

GCF of Numerators i.e. for 682,286 is 22

LCM of denominators i.e. for 704,307 is 216128.

Thus, GCF of Fractions is 22/216128.Finally, GCF of Fractions for 682/704, 286/307 is 22/216128.