GCF of 960/51, 975/254
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 960/51, 975/254 i.e 15/12954 easily. The following is the detailed procedure to determine the greatest common factor of fractions 960/51, 975/254.
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 960/51,975/254?
Given fractions are 960/51,975/254
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 960/51,975/254, numerators are 960,975
Denominators are 51,254
The GCF of 960,975 is 15 .
LCM of 51,254 is 12954.
The greatest common factor of 960/51,975/254 = [GCF of 960,975]/[LCM of 51,254]= 15/12954
Therefore, the GCF of 960/51,975/254 is 15/12954.
To find the highest common factor of 960,975, we have to find the factors of both numbers and list the highest common factor.
The factors of 960 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32, 40, 48, 60, 64, 80, 96, 120, 160, 192, 240, 320, 480, 960
The factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975
The HCF of 960,975 is 15.
Lets's calculate GCF of 960,975
| 3 | 960, 975 |
| 5 | 320, 325 |
| 64, 65 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Greatest Common Factor of 960,975 By Matching Biggest Common Factor Method
Now, list down the factors of 960
:1,2,3,4,5,6,8,10,12,15,16,20,24,30,32,40,48,60,64,80,96,120,160,192,240,320,480,960
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 960,975 . The biggest common factor number is the GCF number.
So the greatest common factor 960,975 is 15.
Lets's calculate LCM of 51,254
Given numbers has no common factors except 1. So, there LCM is their product i.e 12954
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/12954
Therefore, the GCF of Fractions 960/51,975/254 is 15/12954
Least Common Multiple of 51,254 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 51,254 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(51,254) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(51,254) x common factors =1 x 1 = 1
LCM(51,254) = ( 51 × 254 ) / 1
LCM(51,254) = 12954 / 1
LCM(51,254) = 12954
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FAQs on GCF of Fractions of 960/51, 975/254
1. What is the HCF of 960,975?
The HCF of 960,975 is 15
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 960/51, 975/254?
Answer: GCF of Numerators as per given numbers 960/51, 975/254 is
GCF of Numerators i.e. for 960,975 is 15
LCM of denominators i.e. for 51,254 is 12954.
Thus, GCF of Fractions is 15/12954.Finally, GCF of Fractions for 960/51, 975/254 is 15/12954.