GCF of 415/75, 312/5896
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 415/75, 312/5896 i.e 1/442200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 415/75, 312/5896.
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 415/75,312/5896?
Given fractions are 415/75,312/5896
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 415/75,312/5896, numerators are 415,312
Denominators are 75,5896
The GCF of 415,312 is 1 .
LCM of 75,5896 is 442200.
The greatest common factor of 415/75,312/5896 = [GCF of 415,312]/[LCM of 75,5896]= 1/442200
Therefore, the GCF of 415/75,312/5896 is 1/442200.
To find the highest common factor of 415,312, we have to find the factors of both numbers and list the highest common factor.
The factors of 415 are 1, 5, 83, 415
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 415,312 is 1.
Lets's calculate GCF of 415,312
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 415,312 By Matching Biggest Common Factor Method
Now, list down the factors of 415
:1,5,83,415
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 415,312 . The biggest common factor number is the GCF number.
So the greatest common factor 415,312 is 1.
Lets's calculate LCM of 75,5896
Given numbers has no common factors except 1. So, there LCM is their product i.e 442200
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/442200
Therefore, the GCF of Fractions 415/75,312/5896 is 1/442200
Least Common Multiple of 75,5896 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 75,5896 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,5896) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(75,5896) x common factors =1 x 1 = 1
LCM(75,5896) = ( 75 × 5896 ) / 1
LCM(75,5896) = 442200 / 1
LCM(75,5896) = 442200
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FAQs on GCF of Fractions of 415/75, 312/5896
1. What is the HCF of 415,312?
The HCF of 415,312 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 415/75, 312/5896?
Answer: GCF of Numerators as per given numbers 415/75, 312/5896 is
GCF of Numerators i.e. for 415,312 is 1
LCM of denominators i.e. for 75,5896 is 442200.
Thus, GCF of Fractions is 1/442200.Finally, GCF of Fractions for 415/75, 312/5896 is 1/442200.