GCF of 315/38, 615/714
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 315/38, 615/714 i.e 15/13566 easily. The following is the detailed procedure to determine the greatest common factor of fractions 315/38, 615/714.
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 315/38,615/714?
Given fractions are 315/38,615/714
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 315/38,615/714, numerators are 315,615
Denominators are 38,714
The GCF of 315,615 is 15 .
LCM of 38,714 is 13566.
The greatest common factor of 315/38,615/714 = [GCF of 315,615]/[LCM of 38,714]= 15/13566
Therefore, the GCF of 315/38,615/714 is 15/13566.
To find the highest common factor of 315,615, 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 615 are 1, 3, 5, 15, 41, 123, 205, 615
The HCF of 315,615 is 15.
Lets's calculate GCF of 315,615
| 3 | 315, 615 |
| 5 | 105, 205 |
| 21, 41 |
∴ So the GCF of the given numbers is 3 x 5 = 15
Greatest Common Factor of 315,615 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 615
:1,3,5,15,41,123,205,615
Greatest Common Factor
We found the factors 315,615 . The biggest common factor number is the GCF number.
So the greatest common factor 315,615 is 15.
Lets's calculate LCM of 38,714
| 2 | 38, 714 |
| 19, 357 |
∴ So the LCM of the given numbers is 2 x 19 x 357 = 13566
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 15/13566
Therefore, the GCF of Fractions 315/38,615/714 is 15/13566
Least Common Multiple of 38,714 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 38,714 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(38,714) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(38,714) x common factors =2 x 1 = 2
LCM(38,714) = ( 38 × 714 ) / 2
LCM(38,714) = 27132 / 2
LCM(38,714) = 13566
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FAQs on GCF of Fractions of 315/38, 615/714
1. What is the HCF of 315,615?
The HCF of 315,615 is 15
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 315/38, 615/714?
Answer: GCF of Numerators as per given numbers 315/38, 615/714 is
GCF of Numerators i.e. for 315,615 is 15
LCM of denominators i.e. for 38,714 is 13566.
Thus, GCF of Fractions is 15/13566.Finally, GCF of Fractions for 315/38, 615/714 is 15/13566.