GCF of 514/40, 938/24, 314/90
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 514/40, 938/24, 314/90 i.e 2/360 easily. The following is the detailed procedure to determine the greatest common factor of fractions 514/40, 938/24, 314/90.
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 514/40,938/24,314/90?
Given fractions are 514/40,938/24,314/90
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 514/40,938/24,314/90, numerators are 514,938,314
Denominators are 40,24,90
The GCF of 514,938,314 is 2 .
LCM of 40,24,90 is 360.
The greatest common factor of 514/40,938/24,314/90 = [GCF of 514,938,314]/[LCM of 40,24,90]= 2/360
Therefore, the GCF of 514/40,938/24,314/90 is 2/360.
To find the highest common factor of 514,938,314, we have to find the factors of both numbers and list the highest common factor.
The factors of 514 are 1, 2, 257, 514
The factors of 938 are 1, 2, 7, 14, 67, 134, 469, 938
The factors of 314 are 1, 2, 157, 314
The HCF of 514,938,314 is 2.
Lets's calculate GCF of 514,938,314
| 2 | 514, 938, 314 |
| 257, 469, 157 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 514,938,314 By Matching Biggest Common Factor Method
Now, list down the factors of 514
:1,2,257,514
Now, list down the factors of 938
:1,2,7,14,67,134,469,938
Now, list down the factors of 314
:1,2,157,314
Greatest Common Factor
We found the factors 514,938,314 . The biggest common factor number is the GCF number.
So the greatest common factor 514,938,314 is 2.
Lets's calculate LCM of 40,24,90
| 2 | 40, 24, 90 |
| 2 | 20, 12, 45 |
| 2 | 10, 6, 45 |
| 3 | 5, 3, 45 |
| 5 | 5, 1, 15 |
| 1, 1, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 5 x 1 x 1 x 3 = 360
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/360
Therefore, the GCF of Fractions 514/40,938/24,314/90 is 2/360
Least Common Multiple of 40,24,90 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 40,24,90 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,24,90) = 2
common factors(in case of two or more numbers have common factors) = 120
GCF(40,24,90) x common factors =2 x 120 = 240
LCM(40,24,90) = ( 40 × 24 × 90 ) / 240
LCM(40,24,90) = 86400 / 240
LCM(40,24,90) = 360
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 514/40, 938/24, 314/90
1. What is the HCF of 514,938,314?
The HCF of 514,938,314 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 514/40, 938/24, 314/90?
Answer: GCF of Numerators as per given numbers 514/40, 938/24, 314/90 is
GCF of Numerators i.e. for 514,938,314 is 2
LCM of denominators i.e. for 40,24,90 is 360.
Thus, GCF of Fractions is 2/360.Finally, GCF of Fractions for 514/40, 938/24, 314/90 is 2/360.