How to Find GCF of 686/14, 960/3949?

GCF of 686/14, 960/3949

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 686/14, 960/3949 i.e 2/55286 easily. The following is the detailed procedure to determine the greatest common factor of fractions 686/14, 960/3949.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 686/14,960/3949?

Given fractions are 686/14,960/3949

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 686/14,960/3949, numerators are 686,960

Denominators are 14,3949

The GCF of 686,960 is 2 .

LCM of 14,3949 is 55286.

The greatest common factor of 686/14,960/3949 = [GCF of 686,960]/[LCM of 14,3949]= 2/55286

Therefore, the GCF of 686/14,960/3949 is 2/55286.

Greatest Common Factor of 686,960

To find the highest common factor of 686,960, we have to find the factors of both numbers and list the highest common factor.

The factors of 686 are 1, 2, 7, 14, 49, 98, 343, 686

The factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960

The HCF of 686,960 is 2.

Lets's calculate GCF of 686,960

Greatest Common Factor (GCF) of 686,960 By Common Division

2	686, 960
	343, 480

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

Greatest Common Factor of 686,960 By Matching Biggest Common Factor Method

Now, list down the factors of 686

1,2,7,14,49,98,343,686

Now, list down the factors of 960

1,2,3,4,5,6,8,10,12,15,16,20,24,30,32,40,48,60,64,80,96,120,160,192,240,320,480,960

Greatest Common Factor

We found the factors 686,960 . The biggest common factor number is the GCF number.
So the greatest common factor 686,960 is 2.

Lets's calculate LCM of 14,3949

Lowest Common Multiple of 14,3949 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 55286

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/55286

Therefore, the GCF of Fractions 686/14,960/3949 is 2/55286

Least Common Multiple of 14,3949 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 14,3949 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(14,3949) = 1

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

GCF(14,3949) x common factors =1 x 1 = 1

LCM(14,3949) = ( 14 × 3949 ) / 1

LCM(14,3949) = 55286 / 1

LCM(14,3949) = 55286

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 686/14, 960/3949

1. What is the HCF of 686,960?

The HCF of 686,960 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 686/14, 960/3949?

Answer: GCF of Numerators as per given numbers 686/14, 960/3949 is

GCF of Numerators i.e. for 686,960 is 2

LCM of denominators i.e. for 14,3949 is 55286.

Thus, GCF of Fractions is 2/55286.Finally, GCF of Fractions for 686/14, 960/3949 is 2/55286.