Use our free GCF of Fractions Calculator tool to compute the GCF of 312/160, 392/632 i.e 8/12640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 312/160, 392/632.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 312/160,392/632
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 312/160,392/632, numerators are 312,392
Denominators are 160,632
The GCF of 312,392 is 8 .
LCM of 160,632 is 12640.
The greatest common factor of 312/160,392/632 = [GCF of 312,392]/[LCM of 160,632]= 8/12640
Therefore, the GCF of 312/160,392/632 is 8/12640.
To find the highest common factor of 312,392, we have to find the factors of both numbers and list the highest common factor.
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The factors of 392 are 1, 2, 4, 7, 8, 14, 28, 49, 56, 98, 196, 392
The HCF of 312,392 is 8.
Lets's calculate GCF of 312,392
2 | 312, 392 |
2 | 156, 196 |
2 | 78, 98 |
39, 49 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Now, list down the factors of 392
:1,2,4,7,8,14,28,49,56,98,196,392
Greatest Common Factor
We found the factors 312,392 . The biggest common factor number is the GCF number.
So the greatest common factor 312,392 is 8.
Lets's calculate LCM of 160,632
2 | 160, 632 |
2 | 80, 316 |
2 | 40, 158 |
20, 79 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 20 x 79 = 12640
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/12640
Therefore, the GCF of Fractions 312/160,392/632 is 8/12640
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 160,632 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(160,632) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(160,632) x common factors =8 x 1 = 8
LCM(160,632) = ( 160 × 632 ) / 8
LCM(160,632) = 101120 / 8
LCM(160,632) = 12640
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 312,392?
The HCF of 312,392 is 8
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 312/160, 392/632?
Answer: GCF of Numerators as per given numbers 312/160, 392/632 is
GCF of Numerators i.e. for 312,392 is 8
LCM of denominators i.e. for 160,632 is 12640.
Thus, GCF of Fractions is 8/12640.Finally, GCF of Fractions for 312/160, 392/632 is 8/12640.