GCF of 300/96, 975/254
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 300/96, 975/254 i.e 75/12192 easily. The following is the detailed procedure to determine the greatest common factor of fractions 300/96, 975/254.
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 300/96,975/254?
Given fractions are 300/96,975/254
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 300/96,975/254, numerators are 300,975
Denominators are 96,254
The GCF of 300,975 is 75 .
LCM of 96,254 is 12192.
The greatest common factor of 300/96,975/254 = [GCF of 300,975]/[LCM of 96,254]= 75/12192
Therefore, the GCF of 300/96,975/254 is 75/12192.
To find the highest common factor of 300,975, we have to find the factors of both numbers and list the highest common factor.
The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
The factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975
The HCF of 300,975 is 75.
Lets's calculate GCF of 300,975
| 3 | 300, 975 |
| 5 | 100, 325 |
| 5 | 20, 65 |
| 4, 13 |
∴ So the GCF of the given numbers is 3 x 5 x 5 = 75
Greatest Common Factor of 300,975 By Matching Biggest Common Factor Method
Now, list down the factors of 300
:1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300
Now, list down the factors of 975
:1,3,5,13,15,25,39,65,75,195,325,975
Greatest Common Factor
We found the factors 300,975 . The biggest common factor number is the GCF number.
So the greatest common factor 300,975 is 75.
Lets's calculate LCM of 96,254
| 2 | 96, 254 |
| 48, 127 |
∴ So the LCM of the given numbers is 2 x 48 x 127 = 12192
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 75/12192
Therefore, the GCF of Fractions 300/96,975/254 is 75/12192
Least Common Multiple of 96,254 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 96,254 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(96,254) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(96,254) x common factors =2 x 1 = 2
LCM(96,254) = ( 96 × 254 ) / 2
LCM(96,254) = 24384 / 2
LCM(96,254) = 12192
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FAQs on GCF of Fractions of 300/96, 975/254
1. What is the HCF of 300,975?
The HCF of 300,975 is 75
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 300/96, 975/254?
Answer: GCF of Numerators as per given numbers 300/96, 975/254 is
GCF of Numerators i.e. for 300,975 is 75
LCM of denominators i.e. for 96,254 is 12192.
Thus, GCF of Fractions is 75/12192.Finally, GCF of Fractions for 300/96, 975/254 is 75/12192.