GCF of 975/806, 2000/175
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 975/806, 2000/175 i.e 25/141050 easily. The following is the detailed procedure to determine the greatest common factor of fractions 975/806, 2000/175.
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 975/806,2000/175?
Given fractions are 975/806,2000/175
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 975/806,2000/175, numerators are 975,2000
Denominators are 806,175
The GCF of 975,2000 is 25 .
LCM of 806,175 is 141050.
The greatest common factor of 975/806,2000/175 = [GCF of 975,2000]/[LCM of 806,175]= 25/141050
Therefore, the GCF of 975/806,2000/175 is 25/141050.
To find the highest common factor of 975,2000, we have to find the factors of both numbers and list the highest common factor.
The factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975
The factors of 2000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 125, 200, 250, 400, 500, 1000, 2000
The HCF of 975,2000 is 25.
Lets's calculate GCF of 975,2000
| 5 | 975, 2000 |
| 5 | 195, 400 |
| 39, 80 |
∴ So the GCF of the given numbers is 5 x 5 = 25
Greatest Common Factor of 975,2000 By Matching Biggest Common Factor Method
Now, list down the factors of 975
:1,3,5,13,15,25,39,65,75,195,325,975
Now, list down the factors of 2000
:1,2,4,5,8,10,16,20,25,40,50,80,100,125,200,250,400,500,1000,2000
Greatest Common Factor
We found the factors 975,2000 . The biggest common factor number is the GCF number.
So the greatest common factor 975,2000 is 25.
Lets's calculate LCM of 806,175
Given numbers has no common factors except 1. So, there LCM is their product i.e 141050
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 25/141050
Therefore, the GCF of Fractions 975/806,2000/175 is 25/141050
Least Common Multiple of 806,175 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 806,175 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(806,175) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(806,175) x common factors =1 x 1 = 1
LCM(806,175) = ( 806 × 175 ) / 1
LCM(806,175) = 141050 / 1
LCM(806,175) = 141050
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FAQs on GCF of Fractions of 975/806, 2000/175
1. What is the HCF of 975,2000?
The HCF of 975,2000 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 975/806, 2000/175?
Answer: GCF of Numerators as per given numbers 975/806, 2000/175 is
GCF of Numerators i.e. for 975,2000 is 25
LCM of denominators i.e. for 806,175 is 141050.
Thus, GCF of Fractions is 25/141050.Finally, GCF of Fractions for 975/806, 2000/175 is 25/141050.