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GCF of 314/407, 544/677

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 314/407, 544/677 i.e 2/275539 easily. The following is the detailed procedure to determine the greatest common factor of fractions 314/407, 544/677.

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 314/407,544/677?

Given fractions are 314/407,544/677

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 314/407,544/677, numerators are 314,544

Denominators are 407,677

The GCF of 314,544 is 2 .

LCM of 407,677 is 275539.

The greatest common factor of 314/407,544/677 = [GCF of 314,544]/[LCM of 407,677]= 2/275539

Therefore, the GCF of 314/407,544/677 is 2/275539.

Greatest Common Factor of 314,544

To find the highest common factor of 314,544, 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 544 are 1, 2, 4, 8, 16, 17, 32, 34, 68, 136, 272, 544

The HCF of 314,544 is 2.

Lets's calculate GCF of 314,544

Greatest Common Factor (GCF) of 314,544 By Common Division

2 314, 544
157, 272

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

Greatest Common Factor of 314,544 By Matching Biggest Common Factor Method

Greatest Common Factor of 314,544 By Matching Biggest Common Factor Method

Now, list down the factors of 314

:

1,2,157,314

Now, list down the factors of 544

:

1,2,4,8,16,17,32,34,68,136,272,544

Greatest Common Factor

We found the factors 314,544 . The biggest common factor number is the GCF number.
So the greatest common factor 314,544 is 2.

Lets's calculate LCM of 407,677

Lowest Common Multiple of 407,677 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 275539

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/275539

Therefore, the GCF of Fractions 314/407,544/677 is 2/275539

Least Common Multiple of 407,677 with GCF Formula

Least Common Multiple of 407,677 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 407,677 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(407,677) = 1

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

GCF(407,677) x common factors =1 x 1 = 1

LCM(407,677) = ( 407 × 677 ) / 1

LCM(407,677) = 275539 / 1

LCM(407,677) = 275539


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FAQs on GCF of Fractions of 314/407, 544/677

1. What is the HCF of 314,544?

The HCF of 314,544 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 314/407, 544/677?

Answer: GCF of Numerators as per given numbers 314/407, 544/677 is

GCF of Numerators i.e. for 314,544 is 2

LCM of denominators i.e. for 407,677 is 275539.

Thus, GCF of Fractions is 2/275539.Finally, GCF of Fractions for 314/407, 544/677 is 2/275539.