GCF of 900/458, 675/456
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 900/458, 675/456 i.e 225/104424 easily. The following is the detailed procedure to determine the greatest common factor of fractions 900/458, 675/456.
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 900/458,675/456?
Given fractions are 900/458,675/456
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 900/458,675/456, numerators are 900,675
Denominators are 458,456
The GCF of 900,675 is 225 .
LCM of 458,456 is 104424.
The greatest common factor of 900/458,675/456 = [GCF of 900,675]/[LCM of 458,456]= 225/104424
Therefore, the GCF of 900/458,675/456 is 225/104424.
To find the highest common factor of 900,675, we have to find the factors of both numbers and list the highest common factor.
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 factors of 675 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675
The HCF of 900,675 is 225.
Lets's calculate GCF of 900,675
| 3 | 900, 675 |
| 3 | 300, 225 |
| 5 | 100, 75 |
| 5 | 20, 15 |
| 4, 3 |
∴ So the GCF of the given numbers is 3 x 3 x 5 x 5 = 225
Greatest Common Factor of 900,675 By Matching Biggest Common Factor Method
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
Now, list down the factors of 675
:1,3,5,9,15,25,27,45,75,135,225,675
Greatest Common Factor
We found the factors 900,675 . The biggest common factor number is the GCF number.
So the greatest common factor 900,675 is 225.
Lets's calculate LCM of 458,456
| 2 | 458, 456 |
| 229, 228 |
∴ So the LCM of the given numbers is 2 x 229 x 228 = 104424
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 225/104424
Therefore, the GCF of Fractions 900/458,675/456 is 225/104424
Least Common Multiple of 458,456 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 458,456 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(458,456) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(458,456) x common factors =2 x 1 = 2
LCM(458,456) = ( 458 × 456 ) / 2
LCM(458,456) = 208848 / 2
LCM(458,456) = 104424
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FAQs on GCF of Fractions of 900/458, 675/456
1. What is the HCF of 900,675?
The HCF of 900,675 is 225
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 900/458, 675/456?
Answer: GCF of Numerators as per given numbers 900/458, 675/456 is
GCF of Numerators i.e. for 900,675 is 225
LCM of denominators i.e. for 458,456 is 104424.
Thus, GCF of Fractions is 225/104424.Finally, GCF of Fractions for 900/458, 675/456 is 225/104424.