GCF of 275/294, 625/784
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 275/294, 625/784 i.e 25/2352 easily. The following is the detailed procedure to determine the greatest common factor of fractions 275/294, 625/784.
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 275/294,625/784?
Given fractions are 275/294,625/784
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 275/294,625/784, numerators are 275,625
Denominators are 294,784
The GCF of 275,625 is 25 .
LCM of 294,784 is 2352.
The greatest common factor of 275/294,625/784 = [GCF of 275,625]/[LCM of 294,784]= 25/2352
Therefore, the GCF of 275/294,625/784 is 25/2352.
To find the highest common factor of 275,625, we have to find the factors of both numbers and list the highest common factor.
The factors of 275 are 1, 5, 11, 25, 55, 275
The factors of 625 are 1, 5, 25, 125, 625
The HCF of 275,625 is 25.
Lets's calculate GCF of 275,625
| 5 | 275, 625 |
| 5 | 55, 125 |
| 11, 25 |
∴ So the GCF of the given numbers is 5 x 5 = 25
Greatest Common Factor of 275,625 By Matching Biggest Common Factor Method
Now, list down the factors of 275
:1,5,11,25,55,275
Now, list down the factors of 625
:1,5,25,125,625
Greatest Common Factor
We found the factors 275,625 . The biggest common factor number is the GCF number.
So the greatest common factor 275,625 is 25.
Lets's calculate LCM of 294,784
| 2 | 294, 784 |
| 7 | 147, 392 |
| 7 | 21, 56 |
| 3, 8 |
∴ So the LCM of the given numbers is 2 x 7 x 7 x 3 x 8 = 2352
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 25/2352
Therefore, the GCF of Fractions 275/294,625/784 is 25/2352
Least Common Multiple of 294,784 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 294,784 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(294,784) = 98
common factors(in case of two or more numbers have common factors) = 1
GCF(294,784) x common factors =98 x 1 = 98
LCM(294,784) = ( 294 × 784 ) / 98
LCM(294,784) = 230496 / 98
LCM(294,784) = 2352
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FAQs on GCF of Fractions of 275/294, 625/784
1. What is the HCF of 275,625?
The HCF of 275,625 is 25
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 275/294, 625/784?
Answer: GCF of Numerators as per given numbers 275/294, 625/784 is
GCF of Numerators i.e. for 275,625 is 25
LCM of denominators i.e. for 294,784 is 2352.
Thus, GCF of Fractions is 25/2352.Finally, GCF of Fractions for 275/294, 625/784 is 25/2352.