GCF of 800/975, 7217/825
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 800/975, 7217/825 i.e 1/10725 easily. The following is the detailed procedure to determine the greatest common factor of fractions 800/975, 7217/825.
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 800/975,7217/825?
Given fractions are 800/975,7217/825
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 800/975,7217/825, numerators are 800,7217
Denominators are 975,825
The GCF of 800,7217 is 1 .
LCM of 975,825 is 10725.
The greatest common factor of 800/975,7217/825 = [GCF of 800,7217]/[LCM of 975,825]= 1/10725
Therefore, the GCF of 800/975,7217/825 is 1/10725.
To find the highest common factor of 800,7217, we have to find the factors of both numbers and list the highest common factor.
The factors of 800 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 160, 200, 400, 800
The factors of 7217 are 1, 7, 1031, 7217
The HCF of 800,7217 is 1.
Lets's calculate GCF of 800,7217
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 800,7217 By Matching Biggest Common Factor Method
Now, list down the factors of 800
:1,2,4,5,8,10,16,20,25,32,40,50,80,100,160,200,400,800
Now, list down the factors of 7217
:1,7,1031,7217
Greatest Common Factor
We found the factors 800,7217 . The biggest common factor number is the GCF number.
So the greatest common factor 800,7217 is 1.
Lets's calculate LCM of 975,825
| 3 | 975, 825 |
| 5 | 325, 275 |
| 5 | 65, 55 |
| 13, 11 |
∴ So the LCM of the given numbers is 3 x 5 x 5 x 13 x 11 = 10725
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/10725
Therefore, the GCF of Fractions 800/975,7217/825 is 1/10725
Least Common Multiple of 975,825 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 975,825 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(975,825) = 75
common factors(in case of two or more numbers have common factors) = 1
GCF(975,825) x common factors =75 x 1 = 75
LCM(975,825) = ( 975 × 825 ) / 75
LCM(975,825) = 804375 / 75
LCM(975,825) = 10725
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FAQs on GCF of Fractions of 800/975, 7217/825
1. What is the HCF of 800,7217?
The HCF of 800,7217 is 1
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 800/975, 7217/825?
Answer: GCF of Numerators as per given numbers 800/975, 7217/825 is
GCF of Numerators i.e. for 800,7217 is 1
LCM of denominators i.e. for 975,825 is 10725.
Thus, GCF of Fractions is 1/10725.Finally, GCF of Fractions for 800/975, 7217/825 is 1/10725.