GCF of 315/84, 357/1683
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 315/84, 357/1683 i.e 21/47124 easily. The following is the detailed procedure to determine the greatest common factor of fractions 315/84, 357/1683.
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 315/84,357/1683?
Given fractions are 315/84,357/1683
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 315/84,357/1683, numerators are 315,357
Denominators are 84,1683
The GCF of 315,357 is 21 .
LCM of 84,1683 is 47124.
The greatest common factor of 315/84,357/1683 = [GCF of 315,357]/[LCM of 84,1683]= 21/47124
Therefore, the GCF of 315/84,357/1683 is 21/47124.
To find the highest common factor of 315,357, 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 357 are 1, 3, 7, 17, 21, 51, 119, 357
The HCF of 315,357 is 21.
Lets's calculate GCF of 315,357
| 3 | 315, 357 |
| 7 | 105, 119 |
| 15, 17 |
∴ So the GCF of the given numbers is 3 x 7 = 21
Greatest Common Factor of 315,357 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 357
:1,3,7,17,21,51,119,357
Greatest Common Factor
We found the factors 315,357 . The biggest common factor number is the GCF number.
So the greatest common factor 315,357 is 21.
Lets's calculate LCM of 84,1683
| 3 | 84, 1683 |
| 28, 561 |
∴ So the LCM of the given numbers is 3 x 28 x 561 = 47124
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 21/47124
Therefore, the GCF of Fractions 315/84,357/1683 is 21/47124
Least Common Multiple of 84,1683 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 84,1683 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(84,1683) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(84,1683) x common factors =3 x 1 = 3
LCM(84,1683) = ( 84 × 1683 ) / 3
LCM(84,1683) = 141372 / 3
LCM(84,1683) = 47124
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FAQs on GCF of Fractions of 315/84, 357/1683
1. What is the HCF of 315,357?
The HCF of 315,357 is 21
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 315/84, 357/1683?
Answer: GCF of Numerators as per given numbers 315/84, 357/1683 is
GCF of Numerators i.e. for 315,357 is 21
LCM of denominators i.e. for 84,1683 is 47124.
Thus, GCF of Fractions is 21/47124.Finally, GCF of Fractions for 315/84, 357/1683 is 21/47124.