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GCF of 314/709, 669/687

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 314/709, 669/687 i.e 1/487083 easily. The following is the detailed procedure to determine the greatest common factor of fractions 314/709, 669/687.

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 314/709,669/687?

Given fractions are 314/709,669/687

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 314/709,669/687, numerators are 314,669

Denominators are 709,687

The GCF of 314,669 is 1 .

LCM of 709,687 is 487083.

The greatest common factor of 314/709,669/687 = [GCF of 314,669]/[LCM of 709,687]= 1/487083

Therefore, the GCF of 314/709,669/687 is 1/487083.

Greatest Common Factor of 314,669

To find the highest common factor of 314,669, we have to find the factors of both numbers and list the highest common factor.

The factors of 314 are 1, 2, 157, 314

The factors of 669 are 1, 3, 223, 669

The HCF of 314,669 is 1.

Lets's calculate GCF of 314,669

Greatest Common Factor (GCF) of 314,669 By Common Division

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

Greatest Common Factor of 314,669 By Matching Biggest Common Factor Method

Greatest Common Factor of 314,669 By Matching Biggest Common Factor Method

Now, list down the factors of 314

:

1,2,157,314

Now, list down the factors of 669

:

1,3,223,669

Greatest Common Factor

We found the factors 314,669 . The biggest common factor number is the GCF number.
So the greatest common factor 314,669 is 1.

Lets's calculate LCM of 709,687

Lowest Common Multiple of 709,687 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 487083

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/487083

Therefore, the GCF of Fractions 314/709,669/687 is 1/487083

Least Common Multiple of 709,687 with GCF Formula

Least Common Multiple of 709,687 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 709,687 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(709,687) = 1

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

GCF(709,687) x common factors =1 x 1 = 1

LCM(709,687) = ( 709 × 687 ) / 1

LCM(709,687) = 487083 / 1

LCM(709,687) = 487083


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FAQs on GCF of Fractions of 314/709, 669/687

1. What is the HCF of 314,669?

The HCF of 314,669 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 314/709, 669/687?

Answer: GCF of Numerators as per given numbers 314/709, 669/687 is

GCF of Numerators i.e. for 314,669 is 1

LCM of denominators i.e. for 709,687 is 487083.

Thus, GCF of Fractions is 1/487083.Finally, GCF of Fractions for 314/709, 669/687 is 1/487083.