Use our free GCF of Fractions Calculator tool to compute the GCF of 25/64, 252/64, 165/320 i.e 1/320 easily. The following is the detailed procedure to determine the greatest common factor of fractions 25/64, 252/64, 165/320.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 25/64,252/64,165/320
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 25/64,252/64,165/320, numerators are 25,252,165
Denominators are 64,64,320
The GCF of 25,252,165 is 1 .
LCM of 64,64,320 is 320.
The greatest common factor of 25/64,252/64,165/320 = [GCF of 25,252,165]/[LCM of 64,64,320]= 1/320
Therefore, the GCF of 25/64,252/64,165/320 is 1/320.
To find the highest common factor of 25,252,165, we have to find the factors of both numbers and list the highest common factor.
The factors of 25 are 1, 5, 25
The factors of 252 are 1, 2, 3, 4, 6, 7, 9, 12, 14, 18, 21, 28, 36, 42, 63, 84, 126, 252
The factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165
The HCF of 25,252,165 is 1.
Lets's calculate GCF of 25,252,165
∴ So GCF of numbers is 1 because of no common factors present between them.
Now, list down the factors of 25
:1,5,25
Now, list down the factors of 252
:1,2,3,4,6,7,9,12,14,18,21,28,36,42,63,84,126,252
Now, list down the factors of 165
:1,3,5,11,15,33,55,165
Greatest Common Factor
We found the factors 25,252,165 . The biggest common factor number is the GCF number.
So the greatest common factor 25,252,165 is 1.
Lets's calculate LCM of 64,64,320
2 | 64, 64, 320 |
2 | 32, 32, 160 |
2 | 16, 16, 80 |
2 | 8, 8, 40 |
2 | 4, 4, 20 |
2 | 2, 2, 10 |
1, 1, 5 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 2 x 2 x 1 x 1 x 5 = 320
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/320
Therefore, the GCF of Fractions 25/64,252/64,165/320 is 1/320
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 64,64,320 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(64,64,320) = 64
common factors(in case of two or more numbers have common factors) = 64
GCF(64,64,320) x common factors =64 x 64 = 4096
LCM(64,64,320) = ( 64 × 64 × 320 ) / 4096
LCM(64,64,320) = 1310720 / 4096
LCM(64,64,320) = 320
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 25,252,165?
The HCF of 25,252,165 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 25/64, 252/64, 165/320?
Answer: GCF of Numerators as per given numbers 25/64, 252/64, 165/320 is
GCF of Numerators i.e. for 25,252,165 is 1
LCM of denominators i.e. for 64,64,320 is 320.
Thus, GCF of Fractions is 1/320.Finally, GCF of Fractions for 25/64, 252/64, 165/320 is 1/320.