GCF of 1148/375, 2214/978
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1148/375, 2214/978 i.e 82/122250 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1148/375, 2214/978.
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 1148/375,2214/978?
Given fractions are 1148/375,2214/978
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 1148/375,2214/978, numerators are 1148,2214
Denominators are 375,978
The GCF of 1148,2214 is 82 .
LCM of 375,978 is 122250.
The greatest common factor of 1148/375,2214/978 = [GCF of 1148,2214]/[LCM of 375,978]= 82/122250
Therefore, the GCF of 1148/375,2214/978 is 82/122250.
To find the highest common factor of 1148,2214, we have to find the factors of both numbers and list the highest common factor.
The factors of 1148 are 1, 2, 4, 7, 14, 28, 41, 82, 164, 287, 574, 1148
The factors of 2214 are 1, 2, 3, 6, 9, 18, 27, 41, 54, 82, 123, 246, 369, 738, 1107, 2214
The HCF of 1148,2214 is 82.
Lets's calculate GCF of 1148,2214
| 2 | 1148, 2214 |
| 41 | 574, 1107 |
| 14, 27 |
∴ So the GCF of the given numbers is 2 x 41 = 82
Greatest Common Factor of 1148,2214 By Matching Biggest Common Factor Method
Now, list down the factors of 1148
:1,2,4,7,14,28,41,82,164,287,574,1148
Now, list down the factors of 2214
:1,2,3,6,9,18,27,41,54,82,123,246,369,738,1107,2214
Greatest Common Factor
We found the factors 1148,2214 . The biggest common factor number is the GCF number.
So the greatest common factor 1148,2214 is 82.
Lets's calculate LCM of 375,978
| 3 | 375, 978 |
| 125, 326 |
∴ So the LCM of the given numbers is 3 x 125 x 326 = 122250
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 82/122250
Therefore, the GCF of Fractions 1148/375,2214/978 is 82/122250
Least Common Multiple of 375,978 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 375,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(375,978) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(375,978) x common factors =3 x 1 = 3
LCM(375,978) = ( 375 × 978 ) / 3
LCM(375,978) = 366750 / 3
LCM(375,978) = 122250
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FAQs on GCF of Fractions of 1148/375, 2214/978
1. What is the HCF of 1148,2214?
The HCF of 1148,2214 is 82
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 1148/375, 2214/978?
Answer: GCF of Numerators as per given numbers 1148/375, 2214/978 is
GCF of Numerators i.e. for 1148,2214 is 82
LCM of denominators i.e. for 375,978 is 122250.
Thus, GCF of Fractions is 82/122250.Finally, GCF of Fractions for 1148/375, 2214/978 is 82/122250.