How to Find GCF of 196/313, 210/567?

GCF of 196/313, 210/567

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 196/313, 210/567 i.e 14/177471 easily. The following is the detailed procedure to determine the greatest common factor of fractions 196/313, 210/567.

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 196/313,210/567?

Given fractions are 196/313,210/567

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 196/313,210/567, numerators are 196,210

Denominators are 313,567

The GCF of 196,210 is 14 .

LCM of 313,567 is 177471.

The greatest common factor of 196/313,210/567 = [GCF of 196,210]/[LCM of 313,567]= 14/177471

Therefore, the GCF of 196/313,210/567 is 14/177471.

Greatest Common Factor of 196,210

To find the highest common factor of 196,210, we have to find the factors of both numbers and list the highest common factor.

The factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, 196

The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210

The HCF of 196,210 is 14.

Lets's calculate GCF of 196,210

Greatest Common Factor (GCF) of 196,210 By Common Division

2	196, 210
7	98, 105
	14, 15

∴ So the GCF of the given numbers is 2 x 7 = 14

Greatest Common Factor of 196,210 By Matching Biggest Common Factor Method

Now, list down the factors of 196

1,2,4,7,14,28,49,98,196

Now, list down the factors of 210

1,2,3,5,6,7,10,14,15,21,30,35,42,70,105,210

Greatest Common Factor

We found the factors 196,210 . The biggest common factor number is the GCF number.
So the greatest common factor 196,210 is 14.

Lets's calculate LCM of 313,567

Lowest Common Multiple of 313,567 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 177471

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/177471

Therefore, the GCF of Fractions 196/313,210/567 is 14/177471

Least Common Multiple of 313,567 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 313,567 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(313,567) = 1

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

GCF(313,567) x common factors =1 x 1 = 1

LCM(313,567) = ( 313 × 567 ) / 1

LCM(313,567) = 177471 / 1

LCM(313,567) = 177471

GCF of Fractions Calculation Examples

Here are some samples of GCF of Fractions calculations.

FAQs on GCF of Fractions of 196/313, 210/567

1. What is the HCF of 196,210?

The HCF of 196,210 is 14

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 196/313, 210/567?

Answer: GCF of Numerators as per given numbers 196/313, 210/567 is

GCF of Numerators i.e. for 196,210 is 14

LCM of denominators i.e. for 313,567 is 177471.

Thus, GCF of Fractions is 14/177471.Finally, GCF of Fractions for 196/313, 210/567 is 14/177471.