GCF of 945/38, 225/538
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 945/38, 225/538 i.e 45/10222 easily. The following is the detailed procedure to determine the greatest common factor of fractions 945/38, 225/538.
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 945/38,225/538?
Given fractions are 945/38,225/538
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 945/38,225/538, numerators are 945,225
Denominators are 38,538
The GCF of 945,225 is 45 .
LCM of 38,538 is 10222.
The greatest common factor of 945/38,225/538 = [GCF of 945,225]/[LCM of 38,538]= 45/10222
Therefore, the GCF of 945/38,225/538 is 45/10222.
To find the highest common factor of 945,225, we have to find the factors of both numbers and list the highest common factor.
The factors of 945 are 1, 3, 5, 7, 9, 15, 21, 27, 35, 45, 63, 105, 135, 189, 315, 945
The factors of 225 are 1, 3, 5, 9, 15, 25, 45, 75, 225
The HCF of 945,225 is 45.
Lets's calculate GCF of 945,225
| 3 | 945, 225 |
| 3 | 315, 75 |
| 5 | 105, 25 |
| 21, 5 |
∴ So the GCF of the given numbers is 3 x 3 x 5 = 45
Greatest Common Factor of 945,225 By Matching Biggest Common Factor Method
Now, list down the factors of 945
:1,3,5,7,9,15,21,27,35,45,63,105,135,189,315,945
Now, list down the factors of 225
:1,3,5,9,15,25,45,75,225
Greatest Common Factor
We found the factors 945,225 . The biggest common factor number is the GCF number.
So the greatest common factor 945,225 is 45.
Lets's calculate LCM of 38,538
| 2 | 38, 538 |
| 19, 269 |
∴ So the LCM of the given numbers is 2 x 19 x 269 = 10222
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 45/10222
Therefore, the GCF of Fractions 945/38,225/538 is 45/10222
Least Common Multiple of 38,538 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 38,538 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(38,538) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(38,538) x common factors =2 x 1 = 2
LCM(38,538) = ( 38 × 538 ) / 2
LCM(38,538) = 20444 / 2
LCM(38,538) = 10222
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FAQs on GCF of Fractions of 945/38, 225/538
1. What is the HCF of 945,225?
The HCF of 945,225 is 45
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 945/38, 225/538?
Answer: GCF of Numerators as per given numbers 945/38, 225/538 is
GCF of Numerators i.e. for 945,225 is 45
LCM of denominators i.e. for 38,538 is 10222.
Thus, GCF of Fractions is 45/10222.Finally, GCF of Fractions for 945/38, 225/538 is 45/10222.