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GCF of 412/31, 702/679

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 412/31, 702/679 i.e 2/21049 easily. The following is the detailed procedure to determine the greatest common factor of fractions 412/31, 702/679.

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 412/31,702/679?

Given fractions are 412/31,702/679

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 412/31,702/679, numerators are 412,702

Denominators are 31,679

The GCF of 412,702 is 2 .

LCM of 31,679 is 21049.

The greatest common factor of 412/31,702/679 = [GCF of 412,702]/[LCM of 31,679]= 2/21049

Therefore, the GCF of 412/31,702/679 is 2/21049.

Greatest Common Factor of 412,702

To find the highest common factor of 412,702, we have to find the factors of both numbers and list the highest common factor.

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

The factors of 702 are 1, 2, 3, 6, 9, 13, 18, 26, 27, 39, 54, 78, 117, 234, 351, 702

The HCF of 412,702 is 2.

Lets's calculate GCF of 412,702

Greatest Common Factor (GCF) of 412,702 By Common Division

2 412, 702
206, 351

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

Greatest Common Factor of 412,702 By Matching Biggest Common Factor Method

Greatest Common Factor of 412,702 By Matching Biggest Common Factor Method

Now, list down the factors of 412

:

1,2,4,103,206,412

Now, list down the factors of 702

:

1,2,3,6,9,13,18,26,27,39,54,78,117,234,351,702

Greatest Common Factor

We found the factors 412,702 . The biggest common factor number is the GCF number.
So the greatest common factor 412,702 is 2.

Lets's calculate LCM of 31,679

Lowest Common Multiple of 31,679 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 21049

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/21049

Therefore, the GCF of Fractions 412/31,702/679 is 2/21049

Least Common Multiple of 31,679 with GCF Formula

Least Common Multiple of 31,679 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 31,679 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,679) = 1

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

GCF(31,679) x common factors =1 x 1 = 1

LCM(31,679) = ( 31 × 679 ) / 1

LCM(31,679) = 21049 / 1

LCM(31,679) = 21049


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FAQs on GCF of Fractions of 412/31, 702/679

1. What is the HCF of 412,702?

The HCF of 412,702 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 412/31, 702/679?

Answer: GCF of Numerators as per given numbers 412/31, 702/679 is

GCF of Numerators i.e. for 412,702 is 2

LCM of denominators i.e. for 31,679 is 21049.

Thus, GCF of Fractions is 2/21049.Finally, GCF of Fractions for 412/31, 702/679 is 2/21049.