GCF of 8/45, 15/25, 14/322, 540/382
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8/45, 15/25, 14/322, 540/382 i.e 1/13837950 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8/45, 15/25, 14/322, 540/382.
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 8/45,15/25,14/322,540/382?
Given fractions are 8/45,15/25,14/322,540/382
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 8/45,15/25,14/322,540/382, numerators are 8,15,14,540
Denominators are 45,25,322,382
The GCF of 8,15,14,540 is 1 .
LCM of 45,25,322,382 is 13837950.
The greatest common factor of 8/45,15/25,14/322,540/382 = [GCF of 8,15,14,540]/[LCM of 45,25,322,382]= 1/13837950
Therefore, the GCF of 8/45,15/25,14/322,540/382 is 1/13837950.
To find the highest common factor of 8,15,14,540, we have to find the factors of both numbers and list the highest common factor.
The factors of 8 are 1, 2, 4, 8
The factors of 15 are 1, 3, 5, 15
The factors of 14 are 1, 2, 7, 14
The factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540
The HCF of 8,15,14,540 is 1.
Lets's calculate GCF of 8,15,14,540
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 8,15,14,540 By Matching Biggest Common Factor Method
Now, list down the factors of 8
:1,2,4,8
Now, list down the factors of 15
:1,3,5,15
Now, list down the factors of 14
:1,2,7,14
Now, list down the factors of 540
:1,2,3,4,5,6,9,10,12,15,18,20,27,30,36,45,54,60,90,108,135,180,270,540
Greatest Common Factor
We found the factors 8,15,14,540 . The biggest common factor number is the GCF number.
So the greatest common factor 8,15,14,540 is 1.
Lets's calculate LCM of 45,25,322,382
| 2 | 45, 25, 322, 382 |
| 5 | 45, 25, 161, 191 |
| 9, 5, 161, 191 |
∴ So the LCM of the given numbers is 2 x 5 x 9 x 5 x 161 x 191 = 13837950
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/13837950
Therefore, the GCF of Fractions 8/45,15/25,14/322,540/382 is 1/13837950
Least Common Multiple of 45,25,322,382 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 45,25,322,382 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(45,25,322,382) = 1
common factors(in case of two or more numbers have common factors) = 10
GCF(45,25,322,382) x common factors =1 x 10 = 10
LCM(45,25,322,382) = ( 45 × 25 × 322 × 382 ) / 10
LCM(45,25,322,382) = 138379500 / 10
LCM(45,25,322,382) = 13837950
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 8/45, 15/25, 14/322, 540/382
1. What is the HCF of 8,15,14,540?
The HCF of 8,15,14,540 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 8/45, 15/25, 14/322, 540/382?
Answer: GCF of Numerators as per given numbers 8/45, 15/25, 14/322, 540/382 is
GCF of Numerators i.e. for 8,15,14,540 is 1
LCM of denominators i.e. for 45,25,322,382 is 13837950.
Thus, GCF of Fractions is 1/13837950.Finally, GCF of Fractions for 8/45, 15/25, 14/322, 540/382 is 1/13837950.