GCF of 564/30, 165/355
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 564/30, 165/355 i.e 3/2130 easily. The following is the detailed procedure to determine the greatest common factor of fractions 564/30, 165/355.
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 564/30,165/355?
Given fractions are 564/30,165/355
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 564/30,165/355, numerators are 564,165
Denominators are 30,355
The GCF of 564,165 is 3 .
LCM of 30,355 is 2130.
The greatest common factor of 564/30,165/355 = [GCF of 564,165]/[LCM of 30,355]= 3/2130
Therefore, the GCF of 564/30,165/355 is 3/2130.
To find the highest common factor of 564,165, we have to find the factors of both numbers and list the highest common factor.
The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564
The factors of 165 are 1, 3, 5, 11, 15, 33, 55, 165
The HCF of 564,165 is 3.
Lets's calculate GCF of 564,165
| 3 | 564, 165 |
| 188, 55 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 564,165 By Matching Biggest Common Factor Method
Now, list down the factors of 564
:1,2,3,4,6,12,47,94,141,188,282,564
Now, list down the factors of 165
:1,3,5,11,15,33,55,165
Greatest Common Factor
We found the factors 564,165 . The biggest common factor number is the GCF number.
So the greatest common factor 564,165 is 3.
Lets's calculate LCM of 30,355
| 5 | 30, 355 |
| 6, 71 |
∴ So the LCM of the given numbers is 5 x 6 x 71 = 2130
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/2130
Therefore, the GCF of Fractions 564/30,165/355 is 3/2130
Least Common Multiple of 30,355 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 30,355 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,355) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(30,355) x common factors =5 x 1 = 5
LCM(30,355) = ( 30 × 355 ) / 5
LCM(30,355) = 10650 / 5
LCM(30,355) = 2130
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FAQs on GCF of Fractions of 564/30, 165/355
1. What is the HCF of 564,165?
The HCF of 564,165 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 564/30, 165/355?
Answer: GCF of Numerators as per given numbers 564/30, 165/355 is
GCF of Numerators i.e. for 564,165 is 3
LCM of denominators i.e. for 30,355 is 2130.
Thus, GCF of Fractions is 3/2130.Finally, GCF of Fractions for 564/30, 165/355 is 3/2130.