GCF of 315/229, 3960/738
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 315/229, 3960/738 i.e 45/169002 easily. The following is the detailed procedure to determine the greatest common factor of fractions 315/229, 3960/738.
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 315/229,3960/738?
Given fractions are 315/229,3960/738
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 315/229,3960/738, numerators are 315,3960
Denominators are 229,738
The GCF of 315,3960 is 45 .
LCM of 229,738 is 169002.
The greatest common factor of 315/229,3960/738 = [GCF of 315,3960]/[LCM of 229,738]= 45/169002
Therefore, the GCF of 315/229,3960/738 is 45/169002.
To find the highest common factor of 315,3960, 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 3960 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 18, 20, 22, 24, 30, 33, 36, 40, 44, 45, 55, 60, 66, 72, 88, 90, 99, 110, 120, 132, 165, 180, 198, 220, 264, 330, 360, 396, 440, 495, 660, 792, 990, 1320, 1980, 3960
The HCF of 315,3960 is 45.
Lets's calculate GCF of 315,3960
| 3 | 315, 3960 |
| 3 | 105, 1320 |
| 5 | 35, 440 |
| 7, 88 |
∴ So the GCF of the given numbers is 3 x 3 x 5 = 45
Greatest Common Factor of 315,3960 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 3960
:1,2,3,4,5,6,8,9,10,11,12,15,18,20,22,24,30,33,36,40,44,45,55,60,66,72,88,90,99,110,120,132,165,180,198,220,264,330,360,396,440,495,660,792,990,1320,1980,3960
Greatest Common Factor
We found the factors 315,3960 . The biggest common factor number is the GCF number.
So the greatest common factor 315,3960 is 45.
Lets's calculate LCM of 229,738
Given numbers has no common factors except 1. So, there LCM is their product i.e 169002
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 45/169002
Therefore, the GCF of Fractions 315/229,3960/738 is 45/169002
Least Common Multiple of 229,738 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 229,738 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(229,738) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(229,738) x common factors =1 x 1 = 1
LCM(229,738) = ( 229 × 738 ) / 1
LCM(229,738) = 169002 / 1
LCM(229,738) = 169002
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 315/229, 3960/738
1. What is the HCF of 315,3960?
The HCF of 315,3960 is 45
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 315/229, 3960/738?
Answer: GCF of Numerators as per given numbers 315/229, 3960/738 is
GCF of Numerators i.e. for 315,3960 is 45
LCM of denominators i.e. for 229,738 is 169002.
Thus, GCF of Fractions is 45/169002.Finally, GCF of Fractions for 315/229, 3960/738 is 45/169002.