GCF of 315/363, 105/466
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 315/363, 105/466 i.e 105/169158 easily. The following is the detailed procedure to determine the greatest common factor of fractions 315/363, 105/466.
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 315/363,105/466?
Given fractions are 315/363,105/466
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 315/363,105/466, numerators are 315,105
Denominators are 363,466
The GCF of 315,105 is 105 .
LCM of 363,466 is 169158.
The greatest common factor of 315/363,105/466 = [GCF of 315,105]/[LCM of 363,466]= 105/169158
Therefore, the GCF of 315/363,105/466 is 105/169158.
To find the highest common factor of 315,105, we have to find the factors of both numbers and list the highest common factor.
The factors of 315 are 1, 3, 5, 7, 9, 15, 21, 35, 45, 63, 105, 315
The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105
The HCF of 315,105 is 105.
Lets's calculate GCF of 315,105
| 3 | 315, 105 |
| 5 | 105, 35 |
| 7 | 21, 7 |
| 3, 1 |
∴ So the GCF of the given numbers is 3 x 5 x 7 = 105
Greatest Common Factor of 315,105 By Matching Biggest Common Factor Method
Now, list down the factors of 315
:1,3,5,7,9,15,21,35,45,63,105,315
Now, list down the factors of 105
:1,3,5,7,15,21,35,105
Greatest Common Factor
We found the factors 315,105 . The biggest common factor number is the GCF number.
So the greatest common factor 315,105 is 105.
Lets's calculate LCM of 363,466
Given numbers has no common factors except 1. So, there LCM is their product i.e 169158
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 105/169158
Therefore, the GCF of Fractions 315/363,105/466 is 105/169158
Least Common Multiple of 363,466 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 363,466 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(363,466) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(363,466) x common factors =1 x 1 = 1
LCM(363,466) = ( 363 × 466 ) / 1
LCM(363,466) = 169158 / 1
LCM(363,466) = 169158
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FAQs on GCF of Fractions of 315/363, 105/466
1. What is the HCF of 315,105?
The HCF of 315,105 is 105
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 315/363, 105/466?
Answer: GCF of Numerators as per given numbers 315/363, 105/466 is
GCF of Numerators i.e. for 315,105 is 105
LCM of denominators i.e. for 363,466 is 169158.
Thus, GCF of Fractions is 105/169158.Finally, GCF of Fractions for 315/363, 105/466 is 105/169158.