Use our free GCF of Fractions Calculator tool to compute the GCF of 608/386, 864/154 i.e 32/29722 easily. The following is the detailed procedure to determine the greatest common factor of fractions 608/386, 864/154.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 608/386,864/154
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 608/386,864/154, numerators are 608,864
Denominators are 386,154
The GCF of 608,864 is 32 .
LCM of 386,154 is 29722.
The greatest common factor of 608/386,864/154 = [GCF of 608,864]/[LCM of 386,154]= 32/29722
Therefore, the GCF of 608/386,864/154 is 32/29722.
To find the highest common factor of 608,864, we have to find the factors of both numbers and list the highest common factor.
The factors of 608 are 1, 2, 4, 8, 16, 19, 32, 38, 76, 152, 304, 608
The factors of 864 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 72, 96, 108, 144, 216, 288, 432, 864
The HCF of 608,864 is 32.
Lets's calculate GCF of 608,864
2 | 608, 864 |
2 | 304, 432 |
2 | 152, 216 |
2 | 76, 108 |
2 | 38, 54 |
19, 27 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 2 = 32
Now, list down the factors of 608
:1,2,4,8,16,19,32,38,76,152,304,608
Now, list down the factors of 864
:1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,72,96,108,144,216,288,432,864
Greatest Common Factor
We found the factors 608,864 . The biggest common factor number is the GCF number.
So the greatest common factor 608,864 is 32.
Lets's calculate LCM of 386,154
2 | 386, 154 |
193, 77 |
∴ So the LCM of the given numbers is 2 x 193 x 77 = 29722
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 32/29722
Therefore, the GCF of Fractions 608/386,864/154 is 32/29722
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 386,154 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(386,154) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(386,154) x common factors =2 x 1 = 2
LCM(386,154) = ( 386 × 154 ) / 2
LCM(386,154) = 59444 / 2
LCM(386,154) = 29722
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 608,864?
The HCF of 608,864 is 32
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 608/386, 864/154?
Answer: GCF of Numerators as per given numbers 608/386, 864/154 is
GCF of Numerators i.e. for 608,864 is 32
LCM of denominators i.e. for 386,154 is 29722.
Thus, GCF of Fractions is 32/29722.Finally, GCF of Fractions for 608/386, 864/154 is 32/29722.