GCF of 1969/123, 1230/2314
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1969/123, 1230/2314 i.e 1/284622 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1969/123, 1230/2314.
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 1969/123,1230/2314?
Given fractions are 1969/123,1230/2314
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 1969/123,1230/2314, numerators are 1969,1230
Denominators are 123,2314
The GCF of 1969,1230 is 1 .
LCM of 123,2314 is 284622.
The greatest common factor of 1969/123,1230/2314 = [GCF of 1969,1230]/[LCM of 123,2314]= 1/284622
Therefore, the GCF of 1969/123,1230/2314 is 1/284622.
To find the highest common factor of 1969,1230, we have to find the factors of both numbers and list the highest common factor.
The factors of 1969 are 1, 11, 179, 1969
The factors of 1230 are 1, 2, 3, 5, 6, 10, 15, 30, 41, 82, 123, 205, 246, 410, 615, 1230
The HCF of 1969,1230 is 1.
Lets's calculate GCF of 1969,1230
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 1969,1230 By Matching Biggest Common Factor Method
Now, list down the factors of 1969
:1,11,179,1969
Now, list down the factors of 1230
:1,2,3,5,6,10,15,30,41,82,123,205,246,410,615,1230
Greatest Common Factor
We found the factors 1969,1230 . The biggest common factor number is the GCF number.
So the greatest common factor 1969,1230 is 1.
Lets's calculate LCM of 123,2314
Given numbers has no common factors except 1. So, there LCM is their product i.e 284622
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/284622
Therefore, the GCF of Fractions 1969/123,1230/2314 is 1/284622
Least Common Multiple of 123,2314 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 123,2314 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(123,2314) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(123,2314) x common factors =1 x 1 = 1
LCM(123,2314) = ( 123 × 2314 ) / 1
LCM(123,2314) = 284622 / 1
LCM(123,2314) = 284622
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FAQs on GCF of Fractions of 1969/123, 1230/2314
1. What is the HCF of 1969,1230?
The HCF of 1969,1230 is 1
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 1969/123, 1230/2314?
Answer: GCF of Numerators as per given numbers 1969/123, 1230/2314 is
GCF of Numerators i.e. for 1969,1230 is 1
LCM of denominators i.e. for 123,2314 is 284622.
Thus, GCF of Fractions is 1/284622.Finally, GCF of Fractions for 1969/123, 1230/2314 is 1/284622.