GCF of 48/217, 96/413, 600/620
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 48/217, 96/413, 600/620 i.e 24/256060 easily. The following is the detailed procedure to determine the greatest common factor of fractions 48/217, 96/413, 600/620.
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 48/217,96/413,600/620?
Given fractions are 48/217,96/413,600/620
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 48/217,96/413,600/620, numerators are 48,96,600
Denominators are 217,413,620
The GCF of 48,96,600 is 24 .
LCM of 217,413,620 is 256060.
The greatest common factor of 48/217,96/413,600/620 = [GCF of 48,96,600]/[LCM of 217,413,620]= 24/256060
Therefore, the GCF of 48/217,96/413,600/620 is 24/256060.
To find the highest common factor of 48,96,600, we have to find the factors of both numbers and list the highest common factor.
The factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
The factors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
The factors of 600 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 25, 30, 40, 50, 60, 75, 100, 120, 150, 200, 300, 600
The HCF of 48,96,600 is 24.
Lets's calculate GCF of 48,96,600
| 2 | 48, 96, 600 |
| 2 | 24, 48, 300 |
| 2 | 12, 24, 150 |
| 3 | 6, 12, 75 |
| 2, 4, 25 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24
Greatest Common Factor of 48,96,600 By Matching Biggest Common Factor Method
Now, list down the factors of 48
:1,2,3,4,6,8,12,16,24,48
Now, list down the factors of 96
:1,2,3,4,6,8,12,16,24,32,48,96
Now, list down the factors of 600
:1,2,3,4,5,6,8,10,12,15,20,24,25,30,40,50,60,75,100,120,150,200,300,600
Greatest Common Factor
We found the factors 48,96,600 . The biggest common factor number is the GCF number.
So the greatest common factor 48,96,600 is 24.
Lets's calculate LCM of 217,413,620
| 7 | 217, 413, 620 |
| 31 | 31, 59, 620 |
| 1, 59, 20 |
∴ So the LCM of the given numbers is 7 x 31 x 1 x 59 x 20 = 256060
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/256060
Therefore, the GCF of Fractions 48/217,96/413,600/620 is 24/256060
Least Common Multiple of 217,413,620 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 217,413,620 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(217,413,620) = 1
common factors(in case of two or more numbers have common factors) = 217
GCF(217,413,620) x common factors =1 x 217 = 217
LCM(217,413,620) = ( 217 × 413 × 620 ) / 217
LCM(217,413,620) = 55565020 / 217
LCM(217,413,620) = 256060
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 48/217, 96/413, 600/620
1. What is the HCF of 48,96,600?
The HCF of 48,96,600 is 24
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 48/217, 96/413, 600/620?
Answer: GCF of Numerators as per given numbers 48/217, 96/413, 600/620 is
GCF of Numerators i.e. for 48,96,600 is 24
LCM of denominators i.e. for 217,413,620 is 256060.
Thus, GCF of Fractions is 24/256060.Finally, GCF of Fractions for 48/217, 96/413, 600/620 is 24/256060.