Use our free GCF of Fractions Calculator tool to compute the GCF of 342/169, 360/165 i.e 18/27885 easily. The following is the detailed procedure to determine the greatest common factor of fractions 342/169, 360/165.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 342/169,360/165
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 342/169,360/165, numerators are 342,360
Denominators are 169,165
The GCF of 342,360 is 18 .
LCM of 169,165 is 27885.
The greatest common factor of 342/169,360/165 = [GCF of 342,360]/[LCM of 169,165]= 18/27885
Therefore, the GCF of 342/169,360/165 is 18/27885.
To find the highest common factor of 342,360, we have to find the factors of both numbers and list the highest common factor.
The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
The HCF of 342,360 is 18.
Lets's calculate GCF of 342,360
2 | 342, 360 |
3 | 171, 180 |
3 | 57, 60 |
19, 20 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Now, list down the factors of 342
:1,2,3,6,9,18,19,38,57,114,171,342
Now, list down the factors of 360
:1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180,360
Greatest Common Factor
We found the factors 342,360 . The biggest common factor number is the GCF number.
So the greatest common factor 342,360 is 18.
Lets's calculate LCM of 169,165
Given numbers has no common factors except 1. So, there LCM is their product i.e 27885
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/27885
Therefore, the GCF of Fractions 342/169,360/165 is 18/27885
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 169,165 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(169,165) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(169,165) x common factors =1 x 1 = 1
LCM(169,165) = ( 169 × 165 ) / 1
LCM(169,165) = 27885 / 1
LCM(169,165) = 27885
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 342,360?
The HCF of 342,360 is 18
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 342/169, 360/165?
Answer: GCF of Numerators as per given numbers 342/169, 360/165 is
GCF of Numerators i.e. for 342,360 is 18
LCM of denominators i.e. for 169,165 is 27885.
Thus, GCF of Fractions is 18/27885.Finally, GCF of Fractions for 342/169, 360/165 is 18/27885.