GCF of 610/60, 725/1820
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 610/60, 725/1820 i.e 5/5460 easily. The following is the detailed procedure to determine the greatest common factor of fractions 610/60, 725/1820.
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 610/60,725/1820?
Given fractions are 610/60,725/1820
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 610/60,725/1820, numerators are 610,725
Denominators are 60,1820
The GCF of 610,725 is 5 .
LCM of 60,1820 is 5460.
The greatest common factor of 610/60,725/1820 = [GCF of 610,725]/[LCM of 60,1820]= 5/5460
Therefore, the GCF of 610/60,725/1820 is 5/5460.
To find the highest common factor of 610,725, we have to find the factors of both numbers and list the highest common factor.
The factors of 610 are 1, 2, 5, 10, 61, 122, 305, 610
The factors of 725 are 1, 5, 25, 29, 145, 725
The HCF of 610,725 is 5.
Lets's calculate GCF of 610,725
| 5 | 610, 725 |
| 122, 145 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 610,725 By Matching Biggest Common Factor Method
Now, list down the factors of 610
:1,2,5,10,61,122,305,610
Now, list down the factors of 725
:1,5,25,29,145,725
Greatest Common Factor
We found the factors 610,725 . The biggest common factor number is the GCF number.
So the greatest common factor 610,725 is 5.
Lets's calculate LCM of 60,1820
| 2 | 60, 1820 |
| 2 | 30, 910 |
| 5 | 15, 455 |
| 3, 91 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 3 x 91 = 5460
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/5460
Therefore, the GCF of Fractions 610/60,725/1820 is 5/5460
Least Common Multiple of 60,1820 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 60,1820 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(60,1820) = 20
common factors(in case of two or more numbers have common factors) = 1
GCF(60,1820) x common factors =20 x 1 = 20
LCM(60,1820) = ( 60 × 1820 ) / 20
LCM(60,1820) = 109200 / 20
LCM(60,1820) = 5460
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FAQs on GCF of Fractions of 610/60, 725/1820
1. What is the HCF of 610,725?
The HCF of 610,725 is 5
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 610/60, 725/1820?
Answer: GCF of Numerators as per given numbers 610/60, 725/1820 is
GCF of Numerators i.e. for 610,725 is 5
LCM of denominators i.e. for 60,1820 is 5460.
Thus, GCF of Fractions is 5/5460.Finally, GCF of Fractions for 610/60, 725/1820 is 5/5460.