GCF of 228/975, 2016/171
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 228/975, 2016/171 i.e 12/55575 easily. The following is the detailed procedure to determine the greatest common factor of fractions 228/975, 2016/171.
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 228/975,2016/171?
Given fractions are 228/975,2016/171
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 228/975,2016/171, numerators are 228,2016
Denominators are 975,171
The GCF of 228,2016 is 12 .
LCM of 975,171 is 55575.
The greatest common factor of 228/975,2016/171 = [GCF of 228,2016]/[LCM of 975,171]= 12/55575
Therefore, the GCF of 228/975,2016/171 is 12/55575.
To find the highest common factor of 228,2016, we have to find the factors of both numbers and list the highest common factor.
The factors of 228 are 1, 2, 3, 4, 6, 12, 19, 38, 57, 76, 114, 228
The factors of 2016 are 1, 2, 3, 4, 6, 7, 8, 9, 12, 14, 16, 18, 21, 24, 28, 32, 36, 42, 48, 56, 63, 72, 84, 96, 112, 126, 144, 168, 224, 252, 288, 336, 504, 672, 1008, 2016
The HCF of 228,2016 is 12.
Lets's calculate GCF of 228,2016
| 2 | 228, 2016 |
| 2 | 114, 1008 |
| 3 | 57, 504 |
| 19, 168 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 228,2016 By Matching Biggest Common Factor Method
Now, list down the factors of 228
:1,2,3,4,6,12,19,38,57,76,114,228
Now, list down the factors of 2016
:1,2,3,4,6,7,8,9,12,14,16,18,21,24,28,32,36,42,48,56,63,72,84,96,112,126,144,168,224,252,288,336,504,672,1008,2016
Greatest Common Factor
We found the factors 228,2016 . The biggest common factor number is the GCF number.
So the greatest common factor 228,2016 is 12.
Lets's calculate LCM of 975,171
| 3 | 975, 171 |
| 325, 57 |
∴ So the LCM of the given numbers is 3 x 325 x 57 = 55575
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/55575
Therefore, the GCF of Fractions 228/975,2016/171 is 12/55575
Least Common Multiple of 975,171 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 975,171 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(975,171) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(975,171) x common factors =3 x 1 = 3
LCM(975,171) = ( 975 × 171 ) / 3
LCM(975,171) = 166725 / 3
LCM(975,171) = 55575
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FAQs on GCF of Fractions of 228/975, 2016/171
1. What is the HCF of 228,2016?
The HCF of 228,2016 is 12
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 228/975, 2016/171?
Answer: GCF of Numerators as per given numbers 228/975, 2016/171 is
GCF of Numerators i.e. for 228,2016 is 12
LCM of denominators i.e. for 975,171 is 55575.
Thus, GCF of Fractions is 12/55575.Finally, GCF of Fractions for 228/975, 2016/171 is 12/55575.