GCF of 2142/656, 8764/4100
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2142/656, 8764/4100 i.e 14/16400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2142/656, 8764/4100.
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 2142/656,8764/4100?
Given fractions are 2142/656,8764/4100
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 2142/656,8764/4100, numerators are 2142,8764
Denominators are 656,4100
The GCF of 2142,8764 is 14 .
LCM of 656,4100 is 16400.
The greatest common factor of 2142/656,8764/4100 = [GCF of 2142,8764]/[LCM of 656,4100]= 14/16400
Therefore, the GCF of 2142/656,8764/4100 is 14/16400.
To find the highest common factor of 2142,8764, we have to find the factors of both numbers and list the highest common factor.
The factors of 2142 are 1, 2, 3, 6, 7, 9, 14, 17, 18, 21, 34, 42, 51, 63, 102, 119, 126, 153, 238, 306, 357, 714, 1071, 2142
The factors of 8764 are 1, 2, 4, 7, 14, 28, 313, 626, 1252, 2191, 4382, 8764
The HCF of 2142,8764 is 14.
Lets's calculate GCF of 2142,8764
| 2 | 2142, 8764 |
| 7 | 1071, 4382 |
| 153, 626 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 2142,8764 By Matching Biggest Common Factor Method
Now, list down the factors of 2142
:1,2,3,6,7,9,14,17,18,21,34,42,51,63,102,119,126,153,238,306,357,714,1071,2142
Now, list down the factors of 8764
:1,2,4,7,14,28,313,626,1252,2191,4382,8764
Greatest Common Factor
We found the factors 2142,8764 . The biggest common factor number is the GCF number.
So the greatest common factor 2142,8764 is 14.
Lets's calculate LCM of 656,4100
| 2 | 656, 4100 |
| 2 | 328, 2050 |
| 41 | 164, 1025 |
| 4, 25 |
∴ So the LCM of the given numbers is 2 x 2 x 41 x 4 x 25 = 16400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/16400
Therefore, the GCF of Fractions 2142/656,8764/4100 is 14/16400
Least Common Multiple of 656,4100 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 656,4100 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(656,4100) = 164
common factors(in case of two or more numbers have common factors) = 1
GCF(656,4100) x common factors =164 x 1 = 164
LCM(656,4100) = ( 656 × 4100 ) / 164
LCM(656,4100) = 2689600 / 164
LCM(656,4100) = 16400
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FAQs on GCF of Fractions of 2142/656, 8764/4100
1. What is the HCF of 2142,8764?
The HCF of 2142,8764 is 14
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 2142/656, 8764/4100?
Answer: GCF of Numerators as per given numbers 2142/656, 8764/4100 is
GCF of Numerators i.e. for 2142,8764 is 14
LCM of denominators i.e. for 656,4100 is 16400.
Thus, GCF of Fractions is 14/16400.Finally, GCF of Fractions for 2142/656, 8764/4100 is 14/16400.