GCF of 75/48, 978/39, 309/284
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 75/48, 978/39, 309/284 i.e 3/44304 easily. The following is the detailed procedure to determine the greatest common factor of fractions 75/48, 978/39, 309/284.
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 75/48,978/39,309/284?
Given fractions are 75/48,978/39,309/284
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 75/48,978/39,309/284, numerators are 75,978,309
Denominators are 48,39,284
The GCF of 75,978,309 is 3 .
LCM of 48,39,284 is 44304.
The greatest common factor of 75/48,978/39,309/284 = [GCF of 75,978,309]/[LCM of 48,39,284]= 3/44304
Therefore, the GCF of 75/48,978/39,309/284 is 3/44304.
To find the highest common factor of 75,978,309, we have to find the factors of both numbers and list the highest common factor.
The factors of 75 are 1, 3, 5, 15, 25, 75
The factors of 978 are 1, 2, 3, 6, 163, 326, 489, 978
The factors of 309 are 1, 3, 103, 309
The HCF of 75,978,309 is 3.
Lets's calculate GCF of 75,978,309
| 3 | 75, 978, 309 |
| 25, 326, 103 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 75,978,309 By Matching Biggest Common Factor Method
Now, list down the factors of 75
:1,3,5,15,25,75
Now, list down the factors of 978
:1,2,3,6,163,326,489,978
Now, list down the factors of 309
:1,3,103,309
Greatest Common Factor
We found the factors 75,978,309 . The biggest common factor number is the GCF number.
So the greatest common factor 75,978,309 is 3.
Lets's calculate LCM of 48,39,284
| 2 | 48, 39, 284 |
| 2 | 24, 39, 142 |
| 3 | 12, 39, 71 |
| 4, 13, 71 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 4 x 13 x 71 = 44304
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/44304
Therefore, the GCF of Fractions 75/48,978/39,309/284 is 3/44304
Least Common Multiple of 48,39,284 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 48,39,284 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(48,39,284) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(48,39,284) x common factors =1 x 12 = 12
LCM(48,39,284) = ( 48 × 39 × 284 ) / 12
LCM(48,39,284) = 531648 / 12
LCM(48,39,284) = 44304
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FAQs on GCF of Fractions of 75/48, 978/39, 309/284
1. What is the HCF of 75,978,309?
The HCF of 75,978,309 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 75/48, 978/39, 309/284?
Answer: GCF of Numerators as per given numbers 75/48, 978/39, 309/284 is
GCF of Numerators i.e. for 75,978,309 is 3
LCM of denominators i.e. for 48,39,284 is 44304.
Thus, GCF of Fractions is 3/44304.Finally, GCF of Fractions for 75/48, 978/39, 309/284 is 3/44304.