GCF of 2708/144, 3214/459
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2708/144, 3214/459 i.e 2/7344 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2708/144, 3214/459.
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 2708/144,3214/459?
Given fractions are 2708/144,3214/459
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 2708/144,3214/459, numerators are 2708,3214
Denominators are 144,459
The GCF of 2708,3214 is 2 .
LCM of 144,459 is 7344.
The greatest common factor of 2708/144,3214/459 = [GCF of 2708,3214]/[LCM of 144,459]= 2/7344
Therefore, the GCF of 2708/144,3214/459 is 2/7344.
To find the highest common factor of 2708,3214, we have to find the factors of both numbers and list the highest common factor.
The factors of 2708 are 1, 2, 4, 677, 1354, 2708
The factors of 3214 are 1, 2, 1607, 3214
The HCF of 2708,3214 is 2.
Lets's calculate GCF of 2708,3214
| 2 | 2708, 3214 |
| 1354, 1607 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 2708,3214 By Matching Biggest Common Factor Method
Now, list down the factors of 2708
:1,2,4,677,1354,2708
Now, list down the factors of 3214
:1,2,1607,3214
Greatest Common Factor
We found the factors 2708,3214 . The biggest common factor number is the GCF number.
So the greatest common factor 2708,3214 is 2.
Lets's calculate LCM of 144,459
| 3 | 144, 459 |
| 3 | 48, 153 |
| 16, 51 |
∴ So the LCM of the given numbers is 3 x 3 x 16 x 51 = 7344
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/7344
Therefore, the GCF of Fractions 2708/144,3214/459 is 2/7344
Least Common Multiple of 144,459 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 144,459 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(144,459) = 9
common factors(in case of two or more numbers have common factors) = 1
GCF(144,459) x common factors =9 x 1 = 9
LCM(144,459) = ( 144 × 459 ) / 9
LCM(144,459) = 66096 / 9
LCM(144,459) = 7344
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FAQs on GCF of Fractions of 2708/144, 3214/459
1. What is the HCF of 2708,3214?
The HCF of 2708,3214 is 2
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 2708/144, 3214/459?
Answer: GCF of Numerators as per given numbers 2708/144, 3214/459 is
GCF of Numerators i.e. for 2708,3214 is 2
LCM of denominators i.e. for 144,459 is 7344.
Thus, GCF of Fractions is 2/7344.Finally, GCF of Fractions for 2708/144, 3214/459 is 2/7344.