Use our free GCF of Fractions Calculator tool to compute the GCF of 168/19, 564/358 i.e 12/6802 easily. The following is the detailed procedure to determine the greatest common factor of fractions 168/19, 564/358.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 168/19,564/358
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 168/19,564/358, numerators are 168,564
Denominators are 19,358
The GCF of 168,564 is 12 .
LCM of 19,358 is 6802.
The greatest common factor of 168/19,564/358 = [GCF of 168,564]/[LCM of 19,358]= 12/6802
Therefore, the GCF of 168/19,564/358 is 12/6802.
To find the highest common factor of 168,564, we have to find the factors of both numbers and list the highest common factor.
The factors of 168 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 42, 56, 84, 168
The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564
The HCF of 168,564 is 12.
Lets's calculate GCF of 168,564
2 | 168, 564 |
2 | 84, 282 |
3 | 42, 141 |
14, 47 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Now, list down the factors of 168
:1,2,3,4,6,7,8,12,14,21,24,28,42,56,84,168
Now, list down the factors of 564
:1,2,3,4,6,12,47,94,141,188,282,564
Greatest Common Factor
We found the factors 168,564 . The biggest common factor number is the GCF number.
So the greatest common factor 168,564 is 12.
Lets's calculate LCM of 19,358
Given numbers has no common factors except 1. So, there LCM is their product i.e 6802
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/6802
Therefore, the GCF of Fractions 168/19,564/358 is 12/6802
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 19,358 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(19,358) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(19,358) x common factors =1 x 1 = 1
LCM(19,358) = ( 19 × 358 ) / 1
LCM(19,358) = 6802 / 1
LCM(19,358) = 6802
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 168,564?
The HCF of 168,564 is 12
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 168/19, 564/358?
Answer: GCF of Numerators as per given numbers 168/19, 564/358 is
GCF of Numerators i.e. for 168,564 is 12
LCM of denominators i.e. for 19,358 is 6802.
Thus, GCF of Fractions is 12/6802.Finally, GCF of Fractions for 168/19, 564/358 is 12/6802.