GCF of 215/80, 415/152
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 215/80, 415/152 i.e 5/1520 easily. The following is the detailed procedure to determine the greatest common factor of fractions 215/80, 415/152.
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 215/80,415/152?
Given fractions are 215/80,415/152
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 215/80,415/152, numerators are 215,415
Denominators are 80,152
The GCF of 215,415 is 5 .
LCM of 80,152 is 1520.
The greatest common factor of 215/80,415/152 = [GCF of 215,415]/[LCM of 80,152]= 5/1520
Therefore, the GCF of 215/80,415/152 is 5/1520.
To find the highest common factor of 215,415, we have to find the factors of both numbers and list the highest common factor.
The factors of 215 are 1, 5, 43, 215
The factors of 415 are 1, 5, 83, 415
The HCF of 215,415 is 5.
Lets's calculate GCF of 215,415
| 5 | 215, 415 |
| 43, 83 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 215,415 By Matching Biggest Common Factor Method
Now, list down the factors of 215
:1,5,43,215
Now, list down the factors of 415
:1,5,83,415
Greatest Common Factor
We found the factors 215,415 . The biggest common factor number is the GCF number.
So the greatest common factor 215,415 is 5.
Lets's calculate LCM of 80,152
| 2 | 80, 152 |
| 2 | 40, 76 |
| 2 | 20, 38 |
| 10, 19 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 10 x 19 = 1520
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/1520
Therefore, the GCF of Fractions 215/80,415/152 is 5/1520
Least Common Multiple of 80,152 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 80,152 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(80,152) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(80,152) x common factors =8 x 1 = 8
LCM(80,152) = ( 80 × 152 ) / 8
LCM(80,152) = 12160 / 8
LCM(80,152) = 1520
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FAQs on GCF of Fractions of 215/80, 415/152
1. What is the HCF of 215,415?
The HCF of 215,415 is 5
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 215/80, 415/152?
Answer: GCF of Numerators as per given numbers 215/80, 415/152 is
GCF of Numerators i.e. for 215,415 is 5
LCM of denominators i.e. for 80,152 is 1520.
Thus, GCF of Fractions is 5/1520.Finally, GCF of Fractions for 215/80, 415/152 is 5/1520.