GCF of 8510/105, 7978/1325
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8510/105, 7978/1325 i.e 2/27825 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8510/105, 7978/1325.
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 8510/105,7978/1325?
Given fractions are 8510/105,7978/1325
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 8510/105,7978/1325, numerators are 8510,7978
Denominators are 105,1325
The GCF of 8510,7978 is 2 .
LCM of 105,1325 is 27825.
The greatest common factor of 8510/105,7978/1325 = [GCF of 8510,7978]/[LCM of 105,1325]= 2/27825
Therefore, the GCF of 8510/105,7978/1325 is 2/27825.
To find the highest common factor of 8510,7978, we have to find the factors of both numbers and list the highest common factor.
The factors of 8510 are 1, 2, 5, 10, 23, 37, 46, 74, 115, 185, 230, 370, 851, 1702, 4255, 8510
The factors of 7978 are 1, 2, 3989, 7978
The HCF of 8510,7978 is 2.
Lets's calculate GCF of 8510,7978
| 2 | 8510, 7978 |
| 4255, 3989 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 8510,7978 By Matching Biggest Common Factor Method
Now, list down the factors of 8510
:1,2,5,10,23,37,46,74,115,185,230,370,851,1702,4255,8510
Now, list down the factors of 7978
:1,2,3989,7978
Greatest Common Factor
We found the factors 8510,7978 . The biggest common factor number is the GCF number.
So the greatest common factor 8510,7978 is 2.
Lets's calculate LCM of 105,1325
| 5 | 105, 1325 |
| 21, 265 |
∴ So the LCM of the given numbers is 5 x 21 x 265 = 27825
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/27825
Therefore, the GCF of Fractions 8510/105,7978/1325 is 2/27825
Least Common Multiple of 105,1325 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 105,1325 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(105,1325) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(105,1325) x common factors =5 x 1 = 5
LCM(105,1325) = ( 105 × 1325 ) / 5
LCM(105,1325) = 139125 / 5
LCM(105,1325) = 27825
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FAQs on GCF of Fractions of 8510/105, 7978/1325
1. What is the HCF of 8510,7978?
The HCF of 8510,7978 is 2
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 8510/105, 7978/1325?
Answer: GCF of Numerators as per given numbers 8510/105, 7978/1325 is
GCF of Numerators i.e. for 8510,7978 is 2
LCM of denominators i.e. for 105,1325 is 27825.
Thus, GCF of Fractions is 2/27825.Finally, GCF of Fractions for 8510/105, 7978/1325 is 2/27825.