GCF of 9500/84, 8075/874
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9500/84, 8075/874 i.e 475/36708 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9500/84, 8075/874.
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 9500/84,8075/874?
Given fractions are 9500/84,8075/874
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 9500/84,8075/874, numerators are 9500,8075
Denominators are 84,874
The GCF of 9500,8075 is 475 .
LCM of 84,874 is 36708.
The greatest common factor of 9500/84,8075/874 = [GCF of 9500,8075]/[LCM of 84,874]= 475/36708
Therefore, the GCF of 9500/84,8075/874 is 475/36708.
To find the highest common factor of 9500,8075, we have to find the factors of both numbers and list the highest common factor.
The factors of 9500 are 1, 2, 4, 5, 10, 19, 20, 25, 38, 50, 76, 95, 100, 125, 190, 250, 380, 475, 500, 950, 1900, 2375, 4750, 9500
The factors of 8075 are 1, 5, 17, 19, 25, 85, 95, 323, 425, 475, 1615, 8075
The HCF of 9500,8075 is 475.
Lets's calculate GCF of 9500,8075
| 5 | 9500, 8075 |
| 5 | 1900, 1615 |
| 19 | 380, 323 |
| 20, 17 |
∴ So the GCF of the given numbers is 5 x 5 x 19 = 475
Greatest Common Factor of 9500,8075 By Matching Biggest Common Factor Method
Now, list down the factors of 9500
:1,2,4,5,10,19,20,25,38,50,76,95,100,125,190,250,380,475,500,950,1900,2375,4750,9500
Now, list down the factors of 8075
:1,5,17,19,25,85,95,323,425,475,1615,8075
Greatest Common Factor
We found the factors 9500,8075 . The biggest common factor number is the GCF number.
So the greatest common factor 9500,8075 is 475.
Lets's calculate LCM of 84,874
| 2 | 84, 874 |
| 42, 437 |
∴ So the LCM of the given numbers is 2 x 42 x 437 = 36708
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 475/36708
Therefore, the GCF of Fractions 9500/84,8075/874 is 475/36708
Least Common Multiple of 84,874 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 84,874 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,874) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(84,874) x common factors =2 x 1 = 2
LCM(84,874) = ( 84 × 874 ) / 2
LCM(84,874) = 73416 / 2
LCM(84,874) = 36708
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FAQs on GCF of Fractions of 9500/84, 8075/874
1. What is the HCF of 9500,8075?
The HCF of 9500,8075 is 475
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 9500/84, 8075/874?
Answer: GCF of Numerators as per given numbers 9500/84, 8075/874 is
GCF of Numerators i.e. for 9500,8075 is 475
LCM of denominators i.e. for 84,874 is 36708.
Thus, GCF of Fractions is 475/36708.Finally, GCF of Fractions for 9500/84, 8075/874 is 475/36708.