GCF of 96/978, 30/204, 209/374
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 96/978, 30/204, 209/374 i.e 1/365772 easily. The following is the detailed procedure to determine the greatest common factor of fractions 96/978, 30/204, 209/374.
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 96/978,30/204,209/374?
Given fractions are 96/978,30/204,209/374
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 96/978,30/204,209/374, numerators are 96,30,209
Denominators are 978,204,374
The GCF of 96,30,209 is 1 .
LCM of 978,204,374 is 365772.
The greatest common factor of 96/978,30/204,209/374 = [GCF of 96,30,209]/[LCM of 978,204,374]= 1/365772
Therefore, the GCF of 96/978,30/204,209/374 is 1/365772.
To find the highest common factor of 96,30,209, we have to find the factors of both numbers and list the highest common factor.
The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 209 are 1, 11, 19, 209
The HCF of 96,30,209 is 1.
Lets's calculate GCF of 96,30,209
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 96,30,209 By Matching Biggest Common Factor Method
Now, list down the factors of 96
:1,2,3,4,6,8,12,16,24,32,48,96
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 209
:1,11,19,209
Greatest Common Factor
We found the factors 96,30,209 . The biggest common factor number is the GCF number.
So the greatest common factor 96,30,209 is 1.
Lets's calculate LCM of 978,204,374
| 2 | 978, 204, 374 |
| 3 | 489, 102, 187 |
| 17 | 163, 34, 187 |
| 163, 2, 11 |
∴ So the LCM of the given numbers is 2 x 3 x 17 x 163 x 2 x 11 = 365772
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/365772
Therefore, the GCF of Fractions 96/978,30/204,209/374 is 1/365772
Least Common Multiple of 978,204,374 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 978,204,374 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(978,204,374) = 2
common factors(in case of two or more numbers have common factors) = 102
GCF(978,204,374) x common factors =2 x 102 = 204
LCM(978,204,374) = ( 978 × 204 × 374 ) / 204
LCM(978,204,374) = 74617488 / 204
LCM(978,204,374) = 365772
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 96/978, 30/204, 209/374
1. What is the HCF of 96,30,209?
The HCF of 96,30,209 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 96/978, 30/204, 209/374?
Answer: GCF of Numerators as per given numbers 96/978, 30/204, 209/374 is
GCF of Numerators i.e. for 96,30,209 is 1
LCM of denominators i.e. for 978,204,374 is 365772.
Thus, GCF of Fractions is 1/365772.Finally, GCF of Fractions for 96/978, 30/204, 209/374 is 1/365772.