Use our free GCF of Fractions Calculator tool to compute the GCF of 68/312, 72/256, 650/351 i.e 2/89856 easily. The following is the detailed procedure to determine the greatest common factor of fractions 68/312, 72/256, 650/351.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 68/312,72/256,650/351
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 68/312,72/256,650/351, numerators are 68,72,650
Denominators are 312,256,351
The GCF of 68,72,650 is 2 .
LCM of 312,256,351 is 89856.
The greatest common factor of 68/312,72/256,650/351 = [GCF of 68,72,650]/[LCM of 312,256,351]= 2/89856
Therefore, the GCF of 68/312,72/256,650/351 is 2/89856.
To find the highest common factor of 68,72,650, we have to find the factors of both numbers and list the highest common factor.
The factors of 68 are 1, 2, 4, 17, 34, 68
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The factors of 650 are 1, 2, 5, 10, 13, 25, 26, 50, 65, 130, 325, 650
The HCF of 68,72,650 is 2.
Lets's calculate GCF of 68,72,650
2 | 68, 72, 650 |
34, 36, 325 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 68
:1,2,4,17,34,68
Now, list down the factors of 72
:1,2,3,4,6,8,9,12,18,24,36,72
Now, list down the factors of 650
:1,2,5,10,13,25,26,50,65,130,325,650
Greatest Common Factor
We found the factors 68,72,650 . The biggest common factor number is the GCF number.
So the greatest common factor 68,72,650 is 2.
Lets's calculate LCM of 312,256,351
2 | 312, 256, 351 |
2 | 156, 128, 351 |
2 | 78, 64, 351 |
3 | 39, 32, 351 |
13 | 13, 32, 117 |
1, 32, 9 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 3 x 13 x 1 x 32 x 9 = 89856
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/89856
Therefore, the GCF of Fractions 68/312,72/256,650/351 is 2/89856
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 312,256,351 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(312,256,351) = 1
common factors(in case of two or more numbers have common factors) = 312
GCF(312,256,351) x common factors =1 x 312 = 312
LCM(312,256,351) = ( 312 × 256 × 351 ) / 312
LCM(312,256,351) = 28035072 / 312
LCM(312,256,351) = 89856
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 68,72,650?
The HCF of 68,72,650 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 68/312, 72/256, 650/351?
Answer: GCF of Numerators as per given numbers 68/312, 72/256, 650/351 is
GCF of Numerators i.e. for 68,72,650 is 2
LCM of denominators i.e. for 312,256,351 is 89856.
Thus, GCF of Fractions is 2/89856.Finally, GCF of Fractions for 68/312, 72/256, 650/351 is 2/89856.