GCF of 415/825, 2850/420
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 415/825, 2850/420 i.e 5/23100 easily. The following is the detailed procedure to determine the greatest common factor of fractions 415/825, 2850/420.
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 415/825,2850/420?
Given fractions are 415/825,2850/420
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 415/825,2850/420, numerators are 415,2850
Denominators are 825,420
The GCF of 415,2850 is 5 .
LCM of 825,420 is 23100.
The greatest common factor of 415/825,2850/420 = [GCF of 415,2850]/[LCM of 825,420]= 5/23100
Therefore, the GCF of 415/825,2850/420 is 5/23100.
To find the highest common factor of 415,2850, 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 2850 are 1, 2, 3, 5, 6, 10, 15, 19, 25, 30, 38, 50, 57, 75, 95, 114, 150, 190, 285, 475, 570, 950, 1425, 2850
The HCF of 415,2850 is 5.
Lets's calculate GCF of 415,2850
| 5 | 415, 2850 |
| 83, 570 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 415,2850 By Matching Biggest Common Factor Method
Now, list down the factors of 415
:1,5,83,415
Now, list down the factors of 2850
:1,2,3,5,6,10,15,19,25,30,38,50,57,75,95,114,150,190,285,475,570,950,1425,2850
Greatest Common Factor
We found the factors 415,2850 . The biggest common factor number is the GCF number.
So the greatest common factor 415,2850 is 5.
Lets's calculate LCM of 825,420
| 3 | 825, 420 |
| 5 | 275, 140 |
| 55, 28 |
∴ So the LCM of the given numbers is 3 x 5 x 55 x 28 = 23100
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/23100
Therefore, the GCF of Fractions 415/825,2850/420 is 5/23100
Least Common Multiple of 825,420 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 825,420 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(825,420) = 15
common factors(in case of two or more numbers have common factors) = 1
GCF(825,420) x common factors =15 x 1 = 15
LCM(825,420) = ( 825 × 420 ) / 15
LCM(825,420) = 346500 / 15
LCM(825,420) = 23100
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FAQs on GCF of Fractions of 415/825, 2850/420
1. What is the HCF of 415,2850?
The HCF of 415,2850 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 415/825, 2850/420?
Answer: GCF of Numerators as per given numbers 415/825, 2850/420 is
GCF of Numerators i.e. for 415,2850 is 5
LCM of denominators i.e. for 825,420 is 23100.
Thus, GCF of Fractions is 5/23100.Finally, GCF of Fractions for 415/825, 2850/420 is 5/23100.