GCF of 315/85, 228/112
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 315/85, 228/112 i.e 3/9520 easily. The following is the detailed procedure to determine the greatest common factor of fractions 315/85, 228/112.
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 315/85,228/112?
Given fractions are 315/85,228/112
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 315/85,228/112, numerators are 315,228
Denominators are 85,112
The GCF of 315,228 is 3 .
LCM of 85,112 is 9520.
The greatest common factor of 315/85,228/112 = [GCF of 315,228]/[LCM of 85,112]= 3/9520
Therefore, the GCF of 315/85,228/112 is 3/9520.
To find the highest common factor of 315,228, 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 228 are 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228
The HCF of 315,228 is 3.
Lets's calculate GCF of 315,228
| 3 | 315, 228 |
| 105, 76 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 315,228 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 228
:1,2,3,4,6,12,19,38,57,76,114,228
Greatest Common Factor
We found the factors 315,228 . The biggest common factor number is the GCF number.
So the greatest common factor 315,228 is 3.
Lets's calculate LCM of 85,112
Given numbers has no common factors except 1. So, there LCM is their product i.e 9520
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/9520
Therefore, the GCF of Fractions 315/85,228/112 is 3/9520
Least Common Multiple of 85,112 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 85,112 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(85,112) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(85,112) x common factors =1 x 1 = 1
LCM(85,112) = ( 85 × 112 ) / 1
LCM(85,112) = 9520 / 1
LCM(85,112) = 9520
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FAQs on GCF of Fractions of 315/85, 228/112
1. What is the HCF of 315,228?
The HCF of 315,228 is 3
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 315/85, 228/112?
Answer: GCF of Numerators as per given numbers 315/85, 228/112 is
GCF of Numerators i.e. for 315,228 is 3
LCM of denominators i.e. for 85,112 is 9520.
Thus, GCF of Fractions is 3/9520.Finally, GCF of Fractions for 315/85, 228/112 is 3/9520.