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GCF of 668/31, 314/380

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 668/31, 314/380 i.e 2/11780 easily. The following is the detailed procedure to determine the greatest common factor of fractions 668/31, 314/380.

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 668/31,314/380?

Given fractions are 668/31,314/380

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 668/31,314/380, numerators are 668,314

Denominators are 31,380

The GCF of 668,314 is 2 .

LCM of 31,380 is 11780.

The greatest common factor of 668/31,314/380 = [GCF of 668,314]/[LCM of 31,380]= 2/11780

Therefore, the GCF of 668/31,314/380 is 2/11780.

Greatest Common Factor of 668,314

To find the highest common factor of 668,314, we have to find the factors of both numbers and list the highest common factor.

The factors of 668 are 1, 2, 4, 167, 334, 668

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

The HCF of 668,314 is 2.

Lets's calculate GCF of 668,314

Greatest Common Factor (GCF) of 668,314 By Common Division

2 668, 314
334, 157

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

Greatest Common Factor of 668,314 By Matching Biggest Common Factor Method

Greatest Common Factor of 668,314 By Matching Biggest Common Factor Method

Now, list down the factors of 668

:

1,2,4,167,334,668

Now, list down the factors of 314

:

1,2,157,314

Greatest Common Factor

We found the factors 668,314 . The biggest common factor number is the GCF number.
So the greatest common factor 668,314 is 2.

Lets's calculate LCM of 31,380

Lowest Common Multiple of 31,380 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 11780

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/11780

Therefore, the GCF of Fractions 668/31,314/380 is 2/11780

Least Common Multiple of 31,380 with GCF Formula

Least Common Multiple of 31,380 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 31,380 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(31,380) = 1

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

GCF(31,380) x common factors =1 x 1 = 1

LCM(31,380) = ( 31 × 380 ) / 1

LCM(31,380) = 11780 / 1

LCM(31,380) = 11780


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FAQs on GCF of Fractions of 668/31, 314/380

1. What is the HCF of 668,314?

The HCF of 668,314 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 668/31, 314/380?

Answer: GCF of Numerators as per given numbers 668/31, 314/380 is

GCF of Numerators i.e. for 668,314 is 2

LCM of denominators i.e. for 31,380 is 11780.

Thus, GCF of Fractions is 2/11780.Finally, GCF of Fractions for 668/31, 314/380 is 2/11780.