GCF of 30/96, 23/16, 840/96
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 30/96, 23/16, 840/96 i.e 1/96 easily. The following is the detailed procedure to determine the greatest common factor of fractions 30/96, 23/16, 840/96.
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 30/96,23/16,840/96?
Given fractions are 30/96,23/16,840/96
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 30/96,23/16,840/96, numerators are 30,23,840
Denominators are 96,16,96
The GCF of 30,23,840 is 1 .
LCM of 96,16,96 is 96.
The greatest common factor of 30/96,23/16,840/96 = [GCF of 30,23,840]/[LCM of 96,16,96]= 1/96
Therefore, the GCF of 30/96,23/16,840/96 is 1/96.
To find the highest common factor of 30,23,840, we have to find the factors of both numbers and list the highest common factor.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30
The factors of 23 are 1, 23
The factors of 840 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 56, 60, 70, 84, 105, 120, 140, 168, 210, 280, 420, 840
The HCF of 30,23,840 is 1.
Lets's calculate GCF of 30,23,840
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 30,23,840 By Matching Biggest Common Factor Method
Now, list down the factors of 30
:1,2,3,5,6,10,15,30
Now, list down the factors of 23
:1,23
Now, list down the factors of 840
:1,2,3,4,5,6,7,8,10,12,14,15,20,21,24,28,30,35,40,42,56,60,70,84,105,120,140,168,210,280,420,840
Greatest Common Factor
We found the factors 30,23,840 . The biggest common factor number is the GCF number.
So the greatest common factor 30,23,840 is 1.
Lets's calculate LCM of 96,16,96
| 2 | 96, 16, 96 |
| 2 | 48, 8, 48 |
| 2 | 24, 4, 24 |
| 2 | 12, 2, 12 |
| 2 | 6, 1, 6 |
| 3 | 3, 1, 3 |
| 1, 1, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 3 x 1 x 1 x 1 = 96
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/96
Therefore, the GCF of Fractions 30/96,23/16,840/96 is 1/96
Least Common Multiple of 96,16,96 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 96,16,96 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(96,16,96) = 16
common factors(in case of two or more numbers have common factors) = 96
GCF(96,16,96) x common factors =16 x 96 = 1536
LCM(96,16,96) = ( 96 × 16 × 96 ) / 1536
LCM(96,16,96) = 147456 / 1536
LCM(96,16,96) = 96
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 30/96, 23/16, 840/96
1. What is the HCF of 30,23,840?
The HCF of 30,23,840 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 30/96, 23/16, 840/96?
Answer: GCF of Numerators as per given numbers 30/96, 23/16, 840/96 is
GCF of Numerators i.e. for 30,23,840 is 1
LCM of denominators i.e. for 96,16,96 is 96.
Thus, GCF of Fractions is 1/96.Finally, GCF of Fractions for 30/96, 23/16, 840/96 is 1/96.