GCF of 6875/537, 4000/1116
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6875/537, 4000/1116 i.e 125/199764 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6875/537, 4000/1116.
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 6875/537,4000/1116?
Given fractions are 6875/537,4000/1116
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 6875/537,4000/1116, numerators are 6875,4000
Denominators are 537,1116
The GCF of 6875,4000 is 125 .
LCM of 537,1116 is 199764.
The greatest common factor of 6875/537,4000/1116 = [GCF of 6875,4000]/[LCM of 537,1116]= 125/199764
Therefore, the GCF of 6875/537,4000/1116 is 125/199764.
To find the highest common factor of 6875,4000, we have to find the factors of both numbers and list the highest common factor.
The factors of 6875 are 1, 5, 11, 25, 55, 125, 275, 625, 1375, 6875
The factors of 4000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000, 4000
The HCF of 6875,4000 is 125.
Lets's calculate GCF of 6875,4000
| 5 | 6875, 4000 |
| 5 | 1375, 800 |
| 5 | 275, 160 |
| 55, 32 |
∴ So the GCF of the given numbers is 5 x 5 x 5 = 125
Greatest Common Factor of 6875,4000 By Matching Biggest Common Factor Method
Now, list down the factors of 6875
:1,5,11,25,55,125,275,625,1375,6875
Now, list down the factors of 4000
:1,2,4,5,8,10,16,20,25,32,40,50,80,100,125,160,200,250,400,500,800,1000,2000,4000
Greatest Common Factor
We found the factors 6875,4000 . The biggest common factor number is the GCF number.
So the greatest common factor 6875,4000 is 125.
Lets's calculate LCM of 537,1116
| 3 | 537, 1116 |
| 179, 372 |
∴ So the LCM of the given numbers is 3 x 179 x 372 = 199764
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 125/199764
Therefore, the GCF of Fractions 6875/537,4000/1116 is 125/199764
Least Common Multiple of 537,1116 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 537,1116 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(537,1116) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(537,1116) x common factors =3 x 1 = 3
LCM(537,1116) = ( 537 × 1116 ) / 3
LCM(537,1116) = 599292 / 3
LCM(537,1116) = 199764
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FAQs on GCF of Fractions of 6875/537, 4000/1116
1. What is the HCF of 6875,4000?
The HCF of 6875,4000 is 125
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 6875/537, 4000/1116?
Answer: GCF of Numerators as per given numbers 6875/537, 4000/1116 is
GCF of Numerators i.e. for 6875,4000 is 125
LCM of denominators i.e. for 537,1116 is 199764.
Thus, GCF of Fractions is 125/199764.Finally, GCF of Fractions for 6875/537, 4000/1116 is 125/199764.