GCF of 272/75, 900/6865
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 272/75, 900/6865 i.e 4/102975 easily. The following is the detailed procedure to determine the greatest common factor of fractions 272/75, 900/6865.
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 272/75,900/6865?
Given fractions are 272/75,900/6865
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 272/75,900/6865, numerators are 272,900
Denominators are 75,6865
The GCF of 272,900 is 4 .
LCM of 75,6865 is 102975.
The greatest common factor of 272/75,900/6865 = [GCF of 272,900]/[LCM of 75,6865]= 4/102975
Therefore, the GCF of 272/75,900/6865 is 4/102975.
To find the highest common factor of 272,900, we have to find the factors of both numbers and list the highest common factor.
The factors of 272 are 1, 2, 4, 8, 16, 17, 34, 68, 136, 272
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 HCF of 272,900 is 4.
Lets's calculate GCF of 272,900
| 2 | 272, 900 |
| 2 | 136, 450 |
| 68, 225 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 272,900 By Matching Biggest Common Factor Method
Now, list down the factors of 272
:1,2,4,8,16,17,34,68,136,272
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
Greatest Common Factor
We found the factors 272,900 . The biggest common factor number is the GCF number.
So the greatest common factor 272,900 is 4.
Lets's calculate LCM of 75,6865
| 5 | 75, 6865 |
| 15, 1373 |
∴ So the LCM of the given numbers is 5 x 15 x 1373 = 102975
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/102975
Therefore, the GCF of Fractions 272/75,900/6865 is 4/102975
Least Common Multiple of 75,6865 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 75,6865 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,6865) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(75,6865) x common factors =5 x 1 = 5
LCM(75,6865) = ( 75 × 6865 ) / 5
LCM(75,6865) = 514875 / 5
LCM(75,6865) = 102975
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FAQs on GCF of Fractions of 272/75, 900/6865
1. What is the HCF of 272,900?
The HCF of 272,900 is 4
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 272/75, 900/6865?
Answer: GCF of Numerators as per given numbers 272/75, 900/6865 is
GCF of Numerators i.e. for 272,900 is 4
LCM of denominators i.e. for 75,6865 is 102975.
Thus, GCF of Fractions is 4/102975.Finally, GCF of Fractions for 272/75, 900/6865 is 4/102975.