GCF of 225/48, 420/1303
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 225/48, 420/1303 i.e 15/62544 easily. The following is the detailed procedure to determine the greatest common factor of fractions 225/48, 420/1303.
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 225/48,420/1303?
Given fractions are 225/48,420/1303
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 225/48,420/1303, numerators are 225,420
Denominators are 48,1303
The GCF of 225,420 is 15 .
LCM of 48,1303 is 62544.
The greatest common factor of 225/48,420/1303 = [GCF of 225,420]/[LCM of 48,1303]= 15/62544
Therefore, the GCF of 225/48,420/1303 is 15/62544.
To find the highest common factor of 225,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, 225
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 225,420 is 15.
Lets's calculate GCF of 225,420
| 3 | 225, 420 |
| 5 | 75, 140 |
| 15, 28 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Greatest Common Factor of 225,420 By Matching Biggest Common Factor Method
Now, list down the factors of 225
:1,3,5,9,15,25,45,75,225
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 225,420 . The biggest common factor number is the GCF number.
So the greatest common factor 225,420 is 15.
Lets's calculate LCM of 48,1303
Given numbers has no common factors except 1. So, there LCM is their product i.e 62544
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/62544
Therefore, the GCF of Fractions 225/48,420/1303 is 15/62544
Least Common Multiple of 48,1303 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 48,1303 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(48,1303) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(48,1303) x common factors =1 x 1 = 1
LCM(48,1303) = ( 48 × 1303 ) / 1
LCM(48,1303) = 62544 / 1
LCM(48,1303) = 62544
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FAQs on GCF of Fractions of 225/48, 420/1303
1. What is the HCF of 225,420?
The HCF of 225,420 is 15
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 225/48, 420/1303?
Answer: GCF of Numerators as per given numbers 225/48, 420/1303 is
GCF of Numerators i.e. for 225,420 is 15
LCM of denominators i.e. for 48,1303 is 62544.
Thus, GCF of Fractions is 15/62544.Finally, GCF of Fractions for 225/48, 420/1303 is 15/62544.