GCF of 315/196, 1080/475
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 315/196, 1080/475 i.e 45/93100 easily. The following is the detailed procedure to determine the greatest common factor of fractions 315/196, 1080/475.
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 315/196,1080/475?
Given fractions are 315/196,1080/475
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 315/196,1080/475, numerators are 315,1080
Denominators are 196,475
The GCF of 315,1080 is 45 .
LCM of 196,475 is 93100.
The greatest common factor of 315/196,1080/475 = [GCF of 315,1080]/[LCM of 196,475]= 45/93100
Therefore, the GCF of 315/196,1080/475 is 45/93100.
To find the highest common factor of 315,1080, 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 1080 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540, 1080
The HCF of 315,1080 is 45.
Lets's calculate GCF of 315,1080
| 3 | 315, 1080 |
| 3 | 105, 360 |
| 5 | 35, 120 |
| 7, 24 |
∴ So the GCF of the given numbers is 3 x 3 x 5 = 45
Greatest Common Factor of 315,1080 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 1080
:1,2,3,4,5,6,8,9,10,12,15,18,20,24,27,30,36,40,45,54,60,72,90,108,120,135,180,216,270,360,540,1080
Greatest Common Factor
We found the factors 315,1080 . The biggest common factor number is the GCF number.
So the greatest common factor 315,1080 is 45.
Lets's calculate LCM of 196,475
Given numbers has no common factors except 1. So, there LCM is their product i.e 93100
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 45/93100
Therefore, the GCF of Fractions 315/196,1080/475 is 45/93100
Least Common Multiple of 196,475 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 196,475 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(196,475) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(196,475) x common factors =1 x 1 = 1
LCM(196,475) = ( 196 × 475 ) / 1
LCM(196,475) = 93100 / 1
LCM(196,475) = 93100
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FAQs on GCF of Fractions of 315/196, 1080/475
1. What is the HCF of 315,1080?
The HCF of 315,1080 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 315/196, 1080/475?
Answer: GCF of Numerators as per given numbers 315/196, 1080/475 is
GCF of Numerators i.e. for 315,1080 is 45
LCM of denominators i.e. for 196,475 is 93100.
Thus, GCF of Fractions is 45/93100.Finally, GCF of Fractions for 315/196, 1080/475 is 45/93100.