GCF of 2253/470, 4212/978
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2253/470, 4212/978 i.e 3/229830 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2253/470, 4212/978.
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 2253/470,4212/978?
Given fractions are 2253/470,4212/978
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 2253/470,4212/978, numerators are 2253,4212
Denominators are 470,978
The GCF of 2253,4212 is 3 .
LCM of 470,978 is 229830.
The greatest common factor of 2253/470,4212/978 = [GCF of 2253,4212]/[LCM of 470,978]= 3/229830
Therefore, the GCF of 2253/470,4212/978 is 3/229830.
To find the highest common factor of 2253,4212, we have to find the factors of both numbers and list the highest common factor.
The factors of 2253 are 1, 3, 751, 2253
The factors of 4212 are 1, 2, 3, 4, 6, 9, 12, 13, 18, 26, 27, 36, 39, 52, 54, 78, 81, 108, 117, 156, 162, 234, 324, 351, 468, 702, 1053, 1404, 2106, 4212
The HCF of 2253,4212 is 3.
Lets's calculate GCF of 2253,4212
| 3 | 2253, 4212 |
| 751, 1404 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 2253,4212 By Matching Biggest Common Factor Method
Now, list down the factors of 2253
:1,3,751,2253
Now, list down the factors of 4212
:1,2,3,4,6,9,12,13,18,26,27,36,39,52,54,78,81,108,117,156,162,234,324,351,468,702,1053,1404,2106,4212
Greatest Common Factor
We found the factors 2253,4212 . The biggest common factor number is the GCF number.
So the greatest common factor 2253,4212 is 3.
Lets's calculate LCM of 470,978
| 2 | 470, 978 |
| 235, 489 |
∴ So the LCM of the given numbers is 2 x 235 x 489 = 229830
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/229830
Therefore, the GCF of Fractions 2253/470,4212/978 is 3/229830
Least Common Multiple of 470,978 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 470,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(470,978) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(470,978) x common factors =2 x 1 = 2
LCM(470,978) = ( 470 × 978 ) / 2
LCM(470,978) = 459660 / 2
LCM(470,978) = 229830
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FAQs on GCF of Fractions of 2253/470, 4212/978
1. What is the HCF of 2253,4212?
The HCF of 2253,4212 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 2253/470, 4212/978?
Answer: GCF of Numerators as per given numbers 2253/470, 4212/978 is
GCF of Numerators i.e. for 2253,4212 is 3
LCM of denominators i.e. for 470,978 is 229830.
Thus, GCF of Fractions is 3/229830.Finally, GCF of Fractions for 2253/470, 4212/978 is 3/229830.