GCF of 279/75, 144/314
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 279/75, 144/314 i.e 9/23550 easily. The following is the detailed procedure to determine the greatest common factor of fractions 279/75, 144/314.
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 279/75,144/314?
Given fractions are 279/75,144/314
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 279/75,144/314, numerators are 279,144
Denominators are 75,314
The GCF of 279,144 is 9 .
LCM of 75,314 is 23550.
The greatest common factor of 279/75,144/314 = [GCF of 279,144]/[LCM of 75,314]= 9/23550
Therefore, the GCF of 279/75,144/314 is 9/23550.
To find the highest common factor of 279,144, we have to find the factors of both numbers and list the highest common factor.
The factors of 279 are 1, 3, 9, 31, 93, 279
The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
The HCF of 279,144 is 9.
Lets's calculate GCF of 279,144
| 3 | 279, 144 |
| 3 | 93, 48 |
| 31, 16 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 279,144 By Matching Biggest Common Factor Method
Now, list down the factors of 279
:1,3,9,31,93,279
Now, list down the factors of 144
:1,2,3,4,6,8,9,12,16,18,24,36,48,72,144
Greatest Common Factor
We found the factors 279,144 . The biggest common factor number is the GCF number.
So the greatest common factor 279,144 is 9.
Lets's calculate LCM of 75,314
Given numbers has no common factors except 1. So, there LCM is their product i.e 23550
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/23550
Therefore, the GCF of Fractions 279/75,144/314 is 9/23550
Least Common Multiple of 75,314 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 75,314 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,314) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(75,314) x common factors =1 x 1 = 1
LCM(75,314) = ( 75 × 314 ) / 1
LCM(75,314) = 23550 / 1
LCM(75,314) = 23550
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FAQs on GCF of Fractions of 279/75, 144/314
1. What is the HCF of 279,144?
The HCF of 279,144 is 9
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 279/75, 144/314?
Answer: GCF of Numerators as per given numbers 279/75, 144/314 is
GCF of Numerators i.e. for 279,144 is 9
LCM of denominators i.e. for 75,314 is 23550.
Thus, GCF of Fractions is 9/23550.Finally, GCF of Fractions for 279/75, 144/314 is 9/23550.