GCF of 753/54, 144/319
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 753/54, 144/319 i.e 3/17226 easily. The following is the detailed procedure to determine the greatest common factor of fractions 753/54, 144/319.
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 753/54,144/319?
Given fractions are 753/54,144/319
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 753/54,144/319, numerators are 753,144
Denominators are 54,319
The GCF of 753,144 is 3 .
LCM of 54,319 is 17226.
The greatest common factor of 753/54,144/319 = [GCF of 753,144]/[LCM of 54,319]= 3/17226
Therefore, the GCF of 753/54,144/319 is 3/17226.
To find the highest common factor of 753,144, we have to find the factors of both numbers and list the highest common factor.
The factors of 753 are 1, 3, 251, 753
The factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144
The HCF of 753,144 is 3.
Lets's calculate GCF of 753,144
| 3 | 753, 144 |
| 251, 48 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 753,144 By Matching Biggest Common Factor Method
Now, list down the factors of 753
:1,3,251,753
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 753,144 . The biggest common factor number is the GCF number.
So the greatest common factor 753,144 is 3.
Lets's calculate LCM of 54,319
Given numbers has no common factors except 1. So, there LCM is their product i.e 17226
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/17226
Therefore, the GCF of Fractions 753/54,144/319 is 3/17226
Least Common Multiple of 54,319 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 54,319 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(54,319) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(54,319) x common factors =1 x 1 = 1
LCM(54,319) = ( 54 × 319 ) / 1
LCM(54,319) = 17226 / 1
LCM(54,319) = 17226
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FAQs on GCF of Fractions of 753/54, 144/319
1. What is the HCF of 753,144?
The HCF of 753,144 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 753/54, 144/319?
Answer: GCF of Numerators as per given numbers 753/54, 144/319 is
GCF of Numerators i.e. for 753,144 is 3
LCM of denominators i.e. for 54,319 is 17226.
Thus, GCF of Fractions is 3/17226.Finally, GCF of Fractions for 753/54, 144/319 is 3/17226.