GCF of 96/30, 30/17, 400/289
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 96/30, 30/17, 400/289 i.e 2/8670 easily. The following is the detailed procedure to determine the greatest common factor of fractions 96/30, 30/17, 400/289.
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 96/30,30/17,400/289?
Given fractions are 96/30,30/17,400/289
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 96/30,30/17,400/289, numerators are 96,30,400
Denominators are 30,17,289
The GCF of 96,30,400 is 2 .
LCM of 30,17,289 is 8670.
The greatest common factor of 96/30,30/17,400/289 = [GCF of 96,30,400]/[LCM of 30,17,289]= 2/8670
Therefore, the GCF of 96/30,30/17,400/289 is 2/8670.
To find the highest common factor of 96,30,400, 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 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
The HCF of 96,30,400 is 2.
Lets's calculate GCF of 96,30,400
| 2 | 96, 30, 400 |
| 48, 15, 200 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 96,30,400 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 400
:1,2,4,5,8,10,16,20,25,40,50,80,100,200,400
Greatest Common Factor
We found the factors 96,30,400 . The biggest common factor number is the GCF number.
So the greatest common factor 96,30,400 is 2.
Lets's calculate LCM of 30,17,289
| 17 | 30, 17, 289 |
| 30, 1, 17 |
∴ So the LCM of the given numbers is 17 x 30 x 1 x 17 = 8670
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/8670
Therefore, the GCF of Fractions 96/30,30/17,400/289 is 2/8670
Least Common Multiple of 30,17,289 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 30,17,289 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,17,289) = 1
common factors(in case of two or more numbers have common factors) = 17
GCF(30,17,289) x common factors =1 x 17 = 17
LCM(30,17,289) = ( 30 × 17 × 289 ) / 17
LCM(30,17,289) = 147390 / 17
LCM(30,17,289) = 8670
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FAQs on GCF of Fractions of 96/30, 30/17, 400/289
1. What is the HCF of 96,30,400?
The HCF of 96,30,400 is 2
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 96/30, 30/17, 400/289?
Answer: GCF of Numerators as per given numbers 96/30, 30/17, 400/289 is
GCF of Numerators i.e. for 96,30,400 is 2
LCM of denominators i.e. for 30,17,289 is 8670.
Thus, GCF of Fractions is 2/8670.Finally, GCF of Fractions for 96/30, 30/17, 400/289 is 2/8670.