Use our free GCF of Fractions Calculator tool to compute the GCF of 142/164, 708/960 i.e 2/39360 easily. The following is the detailed procedure to determine the greatest common factor of fractions 142/164, 708/960.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 142/164,708/960
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 142/164,708/960, numerators are 142,708
Denominators are 164,960
The GCF of 142,708 is 2 .
LCM of 164,960 is 39360.
The greatest common factor of 142/164,708/960 = [GCF of 142,708]/[LCM of 164,960]= 2/39360
Therefore, the GCF of 142/164,708/960 is 2/39360.
To find the highest common factor of 142,708, we have to find the factors of both numbers and list the highest common factor.
The factors of 142 are 1, 2, 71, 142
The factors of 708 are 1, 2, 3, 4, 6, 12, 59, 118, 177, 236, 354, 708
The HCF of 142,708 is 2.
Lets's calculate GCF of 142,708
2 | 142, 708 |
71, 354 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 142
:1,2,71,142
Now, list down the factors of 708
:1,2,3,4,6,12,59,118,177,236,354,708
Greatest Common Factor
We found the factors 142,708 . The biggest common factor number is the GCF number.
So the greatest common factor 142,708 is 2.
Lets's calculate LCM of 164,960
2 | 164, 960 |
2 | 82, 480 |
41, 240 |
∴ So the LCM of the given numbers is 2 x 2 x 41 x 240 = 39360
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/39360
Therefore, the GCF of Fractions 142/164,708/960 is 2/39360
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 164,960 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(164,960) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(164,960) x common factors =4 x 1 = 4
LCM(164,960) = ( 164 × 960 ) / 4
LCM(164,960) = 157440 / 4
LCM(164,960) = 39360
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 142,708?
The HCF of 142,708 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 142/164, 708/960?
Answer: GCF of Numerators as per given numbers 142/164, 708/960 is
GCF of Numerators i.e. for 142,708 is 2
LCM of denominators i.e. for 164,960 is 39360.
Thus, GCF of Fractions is 2/39360.Finally, GCF of Fractions for 142/164, 708/960 is 2/39360.