GCF of 460/542, 2000/7320
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 460/542, 2000/7320 i.e 20/1983720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 460/542, 2000/7320.
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 460/542,2000/7320?
Given fractions are 460/542,2000/7320
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 460/542,2000/7320, numerators are 460,2000
Denominators are 542,7320
The GCF of 460,2000 is 20 .
LCM of 542,7320 is 1983720.
The greatest common factor of 460/542,2000/7320 = [GCF of 460,2000]/[LCM of 542,7320]= 20/1983720
Therefore, the GCF of 460/542,2000/7320 is 20/1983720.
To find the highest common factor of 460,2000, we have to find the factors of both numbers and list the highest common factor.
The factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460
The factors of 2000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000
The HCF of 460,2000 is 20.
Lets's calculate GCF of 460,2000
| 2 | 460, 2000 |
| 2 | 230, 1000 |
| 5 | 115, 500 |
| 23, 100 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Greatest Common Factor of 460,2000 By Matching Biggest Common Factor Method
Now, list down the factors of 460
:1,2,4,5,10,20,23,46,92,115,230,460
Now, list down the factors of 2000
:1,2,4,5,8,10,16,20,25,40,50,80,100,125,200,250,400,500,1000,2000
Greatest Common Factor
We found the factors 460,2000 . The biggest common factor number is the GCF number.
So the greatest common factor 460,2000 is 20.
Lets's calculate LCM of 542,7320
| 2 | 542, 7320 |
| 271, 3660 |
∴ So the LCM of the given numbers is 2 x 271 x 3660 = 1983720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/1983720
Therefore, the GCF of Fractions 460/542,2000/7320 is 20/1983720
Least Common Multiple of 542,7320 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 542,7320 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(542,7320) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(542,7320) x common factors =2 x 1 = 2
LCM(542,7320) = ( 542 × 7320 ) / 2
LCM(542,7320) = 3967440 / 2
LCM(542,7320) = 1983720
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FAQs on GCF of Fractions of 460/542, 2000/7320
1. What is the HCF of 460,2000?
The HCF of 460,2000 is 20
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 460/542, 2000/7320?
Answer: GCF of Numerators as per given numbers 460/542, 2000/7320 is
GCF of Numerators i.e. for 460,2000 is 20
LCM of denominators i.e. for 542,7320 is 1983720.
Thus, GCF of Fractions is 20/1983720.Finally, GCF of Fractions for 460/542, 2000/7320 is 20/1983720.