GCF of 101/40, 865/75, 230/24
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 101/40, 865/75, 230/24 i.e 1/600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 101/40, 865/75, 230/24.
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 101/40,865/75,230/24?
Given fractions are 101/40,865/75,230/24
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 101/40,865/75,230/24, numerators are 101,865,230
Denominators are 40,75,24
The GCF of 101,865,230 is 1 .
LCM of 40,75,24 is 600.
The greatest common factor of 101/40,865/75,230/24 = [GCF of 101,865,230]/[LCM of 40,75,24]= 1/600
Therefore, the GCF of 101/40,865/75,230/24 is 1/600.
To find the highest common factor of 101,865,230, we have to find the factors of both numbers and list the highest common factor.
The factors of 101 are 1, 101
The factors of 865 are 1, 5, 173, 865
The factors of 230 are 1, 2, 5, 10, 23, 46, 115, 230
The HCF of 101,865,230 is 1.
Lets's calculate GCF of 101,865,230
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 101,865,230 By Matching Biggest Common Factor Method
Now, list down the factors of 101
:1,101
Now, list down the factors of 865
:1,5,173,865
Now, list down the factors of 230
:1,2,5,10,23,46,115,230
Greatest Common Factor
We found the factors 101,865,230 . The biggest common factor number is the GCF number.
So the greatest common factor 101,865,230 is 1.
Lets's calculate LCM of 40,75,24
| 2 | 40, 75, 24 |
| 2 | 20, 75, 12 |
| 2 | 10, 75, 6 |
| 3 | 5, 75, 3 |
| 5 | 5, 25, 1 |
| 1, 5, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 5 x 1 x 5 x 1 = 600
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/600
Therefore, the GCF of Fractions 101/40,865/75,230/24 is 1/600
Least Common Multiple of 40,75,24 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 40,75,24 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,75,24) = 1
common factors(in case of two or more numbers have common factors) = 120
GCF(40,75,24) x common factors =1 x 120 = 120
LCM(40,75,24) = ( 40 × 75 × 24 ) / 120
LCM(40,75,24) = 72000 / 120
LCM(40,75,24) = 600
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 101/40, 865/75, 230/24
1. What is the HCF of 101,865,230?
The HCF of 101,865,230 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 101/40, 865/75, 230/24?
Answer: GCF of Numerators as per given numbers 101/40, 865/75, 230/24 is
GCF of Numerators i.e. for 101,865,230 is 1
LCM of denominators i.e. for 40,75,24 is 600.
Thus, GCF of Fractions is 1/600.Finally, GCF of Fractions for 101/40, 865/75, 230/24 is 1/600.