GCF of 412/30, 520/9985
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 412/30, 520/9985 i.e 4/59910 easily. The following is the detailed procedure to determine the greatest common factor of fractions 412/30, 520/9985.
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 412/30,520/9985?
Given fractions are 412/30,520/9985
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 412/30,520/9985, numerators are 412,520
Denominators are 30,9985
The GCF of 412,520 is 4 .
LCM of 30,9985 is 59910.
The greatest common factor of 412/30,520/9985 = [GCF of 412,520]/[LCM of 30,9985]= 4/59910
Therefore, the GCF of 412/30,520/9985 is 4/59910.
To find the highest common factor of 412,520, we have to find the factors of both numbers and list the highest common factor.
The factors of 412 are 1, 2, 4, 103, 206, 412
The factors of 520 are 1, 2, 4, 5, 8, 10, 13, 20, 26, 40, 52, 65, 104, 130, 260, 520
The HCF of 412,520 is 4.
Lets's calculate GCF of 412,520
| 2 | 412, 520 |
| 2 | 206, 260 |
| 103, 130 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 412,520 By Matching Biggest Common Factor Method
Now, list down the factors of 412
:1,2,4,103,206,412
Now, list down the factors of 520
:1,2,4,5,8,10,13,20,26,40,52,65,104,130,260,520
Greatest Common Factor
We found the factors 412,520 . The biggest common factor number is the GCF number.
So the greatest common factor 412,520 is 4.
Lets's calculate LCM of 30,9985
| 5 | 30, 9985 |
| 6, 1997 |
∴ So the LCM of the given numbers is 5 x 6 x 1997 = 59910
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/59910
Therefore, the GCF of Fractions 412/30,520/9985 is 4/59910
Least Common Multiple of 30,9985 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 30,9985 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(30,9985) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(30,9985) x common factors =5 x 1 = 5
LCM(30,9985) = ( 30 × 9985 ) / 5
LCM(30,9985) = 299550 / 5
LCM(30,9985) = 59910
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FAQs on GCF of Fractions of 412/30, 520/9985
1. What is the HCF of 412,520?
The HCF of 412,520 is 4
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 412/30, 520/9985?
Answer: GCF of Numerators as per given numbers 412/30, 520/9985 is
GCF of Numerators i.e. for 412,520 is 4
LCM of denominators i.e. for 30,9985 is 59910.
Thus, GCF of Fractions is 4/59910.Finally, GCF of Fractions for 412/30, 520/9985 is 4/59910.