GCF of 966/105, 975/695
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 966/105, 975/695 i.e 3/14595 easily. The following is the detailed procedure to determine the greatest common factor of fractions 966/105, 975/695.
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 966/105,975/695?
Given fractions are 966/105,975/695
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 966/105,975/695, numerators are 966,975
Denominators are 105,695
The GCF of 966,975 is 3 .
LCM of 105,695 is 14595.
The greatest common factor of 966/105,975/695 = [GCF of 966,975]/[LCM of 105,695]= 3/14595
Therefore, the GCF of 966/105,975/695 is 3/14595.
To find the highest common factor of 966,975, we have to find the factors of both numbers and list the highest common factor.
The factors of 966 are 1, 2, 3, 6, 7, 14, 21, 23, 42, 46, 69, 138, 161, 322, 483, 966
The factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975
The HCF of 966,975 is 3.
Lets's calculate GCF of 966,975
| 3 | 966, 975 |
| 322, 325 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 966,975 By Matching Biggest Common Factor Method
Now, list down the factors of 966
:1,2,3,6,7,14,21,23,42,46,69,138,161,322,483,966
Now, list down the factors of 975
:1,3,5,13,15,25,39,65,75,195,325,975
Greatest Common Factor
We found the factors 966,975 . The biggest common factor number is the GCF number.
So the greatest common factor 966,975 is 3.
Lets's calculate LCM of 105,695
| 5 | 105, 695 |
| 21, 139 |
∴ So the LCM of the given numbers is 5 x 21 x 139 = 14595
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/14595
Therefore, the GCF of Fractions 966/105,975/695 is 3/14595
Least Common Multiple of 105,695 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 105,695 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(105,695) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(105,695) x common factors =5 x 1 = 5
LCM(105,695) = ( 105 × 695 ) / 5
LCM(105,695) = 72975 / 5
LCM(105,695) = 14595
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FAQs on GCF of Fractions of 966/105, 975/695
1. What is the HCF of 966,975?
The HCF of 966,975 is 3
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 966/105, 975/695?
Answer: GCF of Numerators as per given numbers 966/105, 975/695 is
GCF of Numerators i.e. for 966,975 is 3
LCM of denominators i.e. for 105,695 is 14595.
Thus, GCF of Fractions is 3/14595.Finally, GCF of Fractions for 966/105, 975/695 is 3/14595.