GCF of 135/27, 174/165
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 135/27, 174/165 i.e 3/1485 easily. The following is the detailed procedure to determine the greatest common factor of fractions 135/27, 174/165.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 135/27,174/165?
Given fractions are 135/27,174/165
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 135/27,174/165, numerators are 135,174
Denominators are 27,165
The GCF of 135,174 is 3 .
LCM of 27,165 is 1485.
The greatest common factor of 135/27,174/165 = [GCF of 135,174]/[LCM of 27,165]= 3/1485
Therefore, the GCF of 135/27,174/165 is 3/1485.
To find the highest common factor of 135,174, we have to find the factors of both numbers and list the highest common factor.
The factors of 135 are 1, 3, 5, 9, 15, 27, 45, 135
The factors of 174 are 1, 2, 3, 6, 29, 58, 87, 174
The HCF of 135,174 is 3.
Lets's calculate GCF of 135,174
| 3 | 135, 174 |
| 45, 58 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 135,174 By Matching Biggest Common Factor Method
Now, list down the factors of 135
:1,3,5,9,15,27,45,135
Now, list down the factors of 174
:1,2,3,6,29,58,87,174
Greatest Common Factor
We found the factors 135,174 . The biggest common factor number is the GCF number.
So the greatest common factor 135,174 is 3.
Lets's calculate LCM of 27,165
| 3 | 27, 165 |
| 9, 55 |
∴ So the LCM of the given numbers is 3 x 9 x 55 = 1485
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1485
Therefore, the GCF of Fractions 135/27,174/165 is 3/1485
Least Common Multiple of 27,165 with GCF Formula
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 27,165 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(27,165) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(27,165) x common factors =3 x 1 = 3
LCM(27,165) = ( 27 × 165 ) / 3
LCM(27,165) = 4455 / 3
LCM(27,165) = 1485
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FAQs on GCF of Fractions of 135/27, 174/165
1. What is the HCF of 135,174?
The HCF of 135,174 is 3
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 135/27, 174/165?
Answer: GCF of Numerators as per given numbers 135/27, 174/165 is
GCF of Numerators i.e. for 135,174 is 3
LCM of denominators i.e. for 27,165 is 1485.
Thus, GCF of Fractions is 3/1485.Finally, GCF of Fractions for 135/27, 174/165 is 3/1485.