GCF of 514/775, 900/155, 500/310
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 514/775, 900/155, 500/310 i.e 2/1550 easily. The following is the detailed procedure to determine the greatest common factor of fractions 514/775, 900/155, 500/310.
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 514/775,900/155,500/310?
Given fractions are 514/775,900/155,500/310
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 514/775,900/155,500/310, numerators are 514,900,500
Denominators are 775,155,310
The GCF of 514,900,500 is 2 .
LCM of 775,155,310 is 1550.
The greatest common factor of 514/775,900/155,500/310 = [GCF of 514,900,500]/[LCM of 775,155,310]= 2/1550
Therefore, the GCF of 514/775,900/155,500/310 is 2/1550.
To find the highest common factor of 514,900,500, 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 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900
The factors of 500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500
The HCF of 514,900,500 is 2.
Lets's calculate GCF of 514,900,500
| 2 | 514, 900, 500 |
| 257, 450, 250 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 514,900,500 By Matching Biggest Common Factor Method
Now, list down the factors of 514
:1,2,257,514
Now, list down the factors of 900
:1,2,3,4,5,6,9,10,12,15,18,20,25,30,36,45,50,60,75,90,100,150,180,225,300,450,900
Now, list down the factors of 500
:1,2,4,5,10,20,25,50,100,125,250,500
Greatest Common Factor
We found the factors 514,900,500 . The biggest common factor number is the GCF number.
So the greatest common factor 514,900,500 is 2.
Lets's calculate LCM of 775,155,310
| 5 | 775, 155, 310 |
| 31 | 155, 31, 62 |
| 5, 1, 2 |
∴ So the LCM of the given numbers is 5 x 31 x 5 x 1 x 2 = 1550
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1550
Therefore, the GCF of Fractions 514/775,900/155,500/310 is 2/1550
Least Common Multiple of 775,155,310 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 775,155,310 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(775,155,310) = 155
common factors(in case of two or more numbers have common factors) = 155
GCF(775,155,310) x common factors =155 x 155 = 24025
LCM(775,155,310) = ( 775 × 155 × 310 ) / 24025
LCM(775,155,310) = 37238750 / 24025
LCM(775,155,310) = 1550
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FAQs on GCF of Fractions of 514/775, 900/155, 500/310
1. What is the HCF of 514,900,500?
The HCF of 514,900,500 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 514/775, 900/155, 500/310?
Answer: GCF of Numerators as per given numbers 514/775, 900/155, 500/310 is
GCF of Numerators i.e. for 514,900,500 is 2
LCM of denominators i.e. for 775,155,310 is 1550.
Thus, GCF of Fractions is 2/1550.Finally, GCF of Fractions for 514/775, 900/155, 500/310 is 2/1550.