GCF of 243/978, 507/419
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 243/978, 507/419 i.e 3/409782 easily. The following is the detailed procedure to determine the greatest common factor of fractions 243/978, 507/419.
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 243/978,507/419?
Given fractions are 243/978,507/419
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 243/978,507/419, numerators are 243,507
Denominators are 978,419
The GCF of 243,507 is 3 .
LCM of 978,419 is 409782.
The greatest common factor of 243/978,507/419 = [GCF of 243,507]/[LCM of 978,419]= 3/409782
Therefore, the GCF of 243/978,507/419 is 3/409782.
To find the highest common factor of 243,507, we have to find the factors of both numbers and list the highest common factor.
The factors of 243 are 1, 3, 9, 27, 81, 243
The factors of 507 are 1, 3, 13, 39, 169, 507
The HCF of 243,507 is 3.
Lets's calculate GCF of 243,507
| 3 | 243, 507 |
| 81, 169 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 243,507 By Matching Biggest Common Factor Method
Now, list down the factors of 243
:1,3,9,27,81,243
Now, list down the factors of 507
:1,3,13,39,169,507
Greatest Common Factor
We found the factors 243,507 . The biggest common factor number is the GCF number.
So the greatest common factor 243,507 is 3.
Lets's calculate LCM of 978,419
Given numbers has no common factors except 1. So, there LCM is their product i.e 409782
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/409782
Therefore, the GCF of Fractions 243/978,507/419 is 3/409782
Least Common Multiple of 978,419 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 978,419 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(978,419) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(978,419) x common factors =1 x 1 = 1
LCM(978,419) = ( 978 × 419 ) / 1
LCM(978,419) = 409782 / 1
LCM(978,419) = 409782
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 243/978, 507/419
1. What is the HCF of 243,507?
The HCF of 243,507 is 3
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 243/978, 507/419?
Answer: GCF of Numerators as per given numbers 243/978, 507/419 is
GCF of Numerators i.e. for 243,507 is 3
LCM of denominators i.e. for 978,419 is 409782.
Thus, GCF of Fractions is 3/409782.Finally, GCF of Fractions for 243/978, 507/419 is 3/409782.