GCF of 9905/466, 1680/7652
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9905/466, 1680/7652 i.e 35/1782916 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9905/466, 1680/7652.
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 9905/466,1680/7652?
Given fractions are 9905/466,1680/7652
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 9905/466,1680/7652, numerators are 9905,1680
Denominators are 466,7652
The GCF of 9905,1680 is 35 .
LCM of 466,7652 is 1782916.
The greatest common factor of 9905/466,1680/7652 = [GCF of 9905,1680]/[LCM of 466,7652]= 35/1782916
Therefore, the GCF of 9905/466,1680/7652 is 35/1782916.
To find the highest common factor of 9905,1680, we have to find the factors of both numbers and list the highest common factor.
The factors of 9905 are 1, 5, 7, 35, 283, 1415, 1981, 9905
The factors of 1680 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 28, 30, 35, 40, 42, 48, 56, 60, 70, 80, 84, 105, 112, 120, 140, 168, 210, 240, 280, 336, 420, 560, 840, 1680
The HCF of 9905,1680 is 35.
Lets's calculate GCF of 9905,1680
| 5 | 9905, 1680 |
| 7 | 1981, 336 |
| 283, 48 |
∴ So the GCF of the given numbers is 5 x 7 = 35
Greatest Common Factor of 9905,1680 By Matching Biggest Common Factor Method
Now, list down the factors of 9905
:1,5,7,35,283,1415,1981,9905
Now, list down the factors of 1680
:1,2,3,4,5,6,7,8,10,12,14,15,16,20,21,24,28,30,35,40,42,48,56,60,70,80,84,105,112,120,140,168,210,240,280,336,420,560,840,1680
Greatest Common Factor
We found the factors 9905,1680 . The biggest common factor number is the GCF number.
So the greatest common factor 9905,1680 is 35.
Lets's calculate LCM of 466,7652
| 2 | 466, 7652 |
| 233, 3826 |
∴ So the LCM of the given numbers is 2 x 233 x 3826 = 1782916
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 35/1782916
Therefore, the GCF of Fractions 9905/466,1680/7652 is 35/1782916
Least Common Multiple of 466,7652 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 466,7652 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(466,7652) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(466,7652) x common factors =2 x 1 = 2
LCM(466,7652) = ( 466 × 7652 ) / 2
LCM(466,7652) = 3565832 / 2
LCM(466,7652) = 1782916
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FAQs on GCF of Fractions of 9905/466, 1680/7652
1. What is the HCF of 9905,1680?
The HCF of 9905,1680 is 35
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 9905/466, 1680/7652?
Answer: GCF of Numerators as per given numbers 9905/466, 1680/7652 is
GCF of Numerators i.e. for 9905,1680 is 35
LCM of denominators i.e. for 466,7652 is 1782916.
Thus, GCF of Fractions is 35/1782916.Finally, GCF of Fractions for 9905/466, 1680/7652 is 35/1782916.