GCF of 228/289, 2014/1508
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 228/289, 2014/1508 i.e 38/435812 easily. The following is the detailed procedure to determine the greatest common factor of fractions 228/289, 2014/1508.
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 228/289,2014/1508?
Given fractions are 228/289,2014/1508
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 228/289,2014/1508, numerators are 228,2014
Denominators are 289,1508
The GCF of 228,2014 is 38 .
LCM of 289,1508 is 435812.
The greatest common factor of 228/289,2014/1508 = [GCF of 228,2014]/[LCM of 289,1508]= 38/435812
Therefore, the GCF of 228/289,2014/1508 is 38/435812.
To find the highest common factor of 228,2014, we have to find the factors of both numbers and list the highest common factor.
The factors of 228 are 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228
The factors of 2014 are 1, 2, 19, 38, 53, 106, 1007, 2014
The HCF of 228,2014 is 38.
Lets's calculate GCF of 228,2014
| 2 | 228, 2014 |
| 19 | 114, 1007 |
| 6, 53 |
∴ So the GCF of the given numbers is 2 x 19 = 38
Greatest Common Factor of 228,2014 By Matching Biggest Common Factor Method
Now, list down the factors of 228
:1,2,3,4,6,12,19,38,57,76,114,228
Now, list down the factors of 2014
:1,2,19,38,53,106,1007,2014
Greatest Common Factor
We found the factors 228,2014 . The biggest common factor number is the GCF number.
So the greatest common factor 228,2014 is 38.
Lets's calculate LCM of 289,1508
Given numbers has no common factors except 1. So, there LCM is their product i.e 435812
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 38/435812
Therefore, the GCF of Fractions 228/289,2014/1508 is 38/435812
Least Common Multiple of 289,1508 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 289,1508 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(289,1508) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(289,1508) x common factors =1 x 1 = 1
LCM(289,1508) = ( 289 × 1508 ) / 1
LCM(289,1508) = 435812 / 1
LCM(289,1508) = 435812
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FAQs on GCF of Fractions of 228/289, 2014/1508
1. What is the HCF of 228,2014?
The HCF of 228,2014 is 38
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 228/289, 2014/1508?
Answer: GCF of Numerators as per given numbers 228/289, 2014/1508 is
GCF of Numerators i.e. for 228,2014 is 38
LCM of denominators i.e. for 289,1508 is 435812.
Thus, GCF of Fractions is 38/435812.Finally, GCF of Fractions for 228/289, 2014/1508 is 38/435812.