GCF of 225/54, 774/208
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 225/54, 774/208 i.e 9/5616 easily. The following is the detailed procedure to determine the greatest common factor of fractions 225/54, 774/208.
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 225/54,774/208?
Given fractions are 225/54,774/208
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 225/54,774/208, numerators are 225,774
Denominators are 54,208
The GCF of 225,774 is 9 .
LCM of 54,208 is 5616.
The greatest common factor of 225/54,774/208 = [GCF of 225,774]/[LCM of 54,208]= 9/5616
Therefore, the GCF of 225/54,774/208 is 9/5616.
To find the highest common factor of 225,774, 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 774 are 1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, 774
The HCF of 225,774 is 9.
Lets's calculate GCF of 225,774
| 3 | 225, 774 |
| 3 | 75, 258 |
| 25, 86 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 225,774 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 774
:1,2,3,6,9,18,43,86,129,258,387,774
Greatest Common Factor
We found the factors 225,774 . The biggest common factor number is the GCF number.
So the greatest common factor 225,774 is 9.
Lets's calculate LCM of 54,208
| 2 | 54, 208 |
| 27, 104 |
∴ So the LCM of the given numbers is 2 x 27 x 104 = 5616
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/5616
Therefore, the GCF of Fractions 225/54,774/208 is 9/5616
Least Common Multiple of 54,208 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 54,208 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,208) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(54,208) x common factors =2 x 1 = 2
LCM(54,208) = ( 54 × 208 ) / 2
LCM(54,208) = 11232 / 2
LCM(54,208) = 5616
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FAQs on GCF of Fractions of 225/54, 774/208
1. What is the HCF of 225,774?
The HCF of 225,774 is 9
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 225/54, 774/208?
Answer: GCF of Numerators as per given numbers 225/54, 774/208 is
GCF of Numerators i.e. for 225,774 is 9
LCM of denominators i.e. for 54,208 is 5616.
Thus, GCF of Fractions is 9/5616.Finally, GCF of Fractions for 225/54, 774/208 is 9/5616.