GCF of 367/69, 309/978
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 367/69, 309/978 i.e 1/22494 easily. The following is the detailed procedure to determine the greatest common factor of fractions 367/69, 309/978.
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 367/69,309/978?
Given fractions are 367/69,309/978
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 367/69,309/978, numerators are 367,309
Denominators are 69,978
The GCF of 367,309 is 1 .
LCM of 69,978 is 22494.
The greatest common factor of 367/69,309/978 = [GCF of 367,309]/[LCM of 69,978]= 1/22494
Therefore, the GCF of 367/69,309/978 is 1/22494.
To find the highest common factor of 367,309, we have to find the factors of both numbers and list the highest common factor.
The factors of 367 are 1, 367
The factors of 309 are 1, 3, 103, 309
The HCF of 367,309 is 1.
Lets's calculate GCF of 367,309
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 367,309 By Matching Biggest Common Factor Method
Now, list down the factors of 367
:1,367
Now, list down the factors of 309
:1,3,103,309
Greatest Common Factor
We found the factors 367,309 . The biggest common factor number is the GCF number.
So the greatest common factor 367,309 is 1.
Lets's calculate LCM of 69,978
| 3 | 69, 978 |
| 23, 326 |
∴ So the LCM of the given numbers is 3 x 23 x 326 = 22494
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/22494
Therefore, the GCF of Fractions 367/69,309/978 is 1/22494
Least Common Multiple of 69,978 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 69,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(69,978) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(69,978) x common factors =3 x 1 = 3
LCM(69,978) = ( 69 × 978 ) / 3
LCM(69,978) = 67482 / 3
LCM(69,978) = 22494
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 367/69, 309/978
1. What is the HCF of 367,309?
The HCF of 367,309 is 1
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 367/69, 309/978?
Answer: GCF of Numerators as per given numbers 367/69, 309/978 is
GCF of Numerators i.e. for 367,309 is 1
LCM of denominators i.e. for 69,978 is 22494.
Thus, GCF of Fractions is 1/22494.Finally, GCF of Fractions for 367/69, 309/978 is 1/22494.