GCF of 2128/568, 9198/2214
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2128/568, 9198/2214 i.e 14/628776 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2128/568, 9198/2214.
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 2128/568,9198/2214?
Given fractions are 2128/568,9198/2214
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 2128/568,9198/2214, numerators are 2128,9198
Denominators are 568,2214
The GCF of 2128,9198 is 14 .
LCM of 568,2214 is 628776.
The greatest common factor of 2128/568,9198/2214 = [GCF of 2128,9198]/[LCM of 568,2214]= 14/628776
Therefore, the GCF of 2128/568,9198/2214 is 14/628776.
To find the highest common factor of 2128,9198, we have to find the factors of both numbers and list the highest common factor.
The factors of 2128 are 1, 2, 4, 7, 8, 14, 16, 19, 28, 38, 56, 76, 112, 133, 152, 266, 304, 532, 1064, 2128
The factors of 9198 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 42, 63, 73, 126, 146, 219, 438, 511, 657, 1022, 1314, 1533, 3066, 4599, 9198
The HCF of 2128,9198 is 14.
Lets's calculate GCF of 2128,9198
| 2 | 2128, 9198 |
| 7 | 1064, 4599 |
| 152, 657 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 2128,9198 By Matching Biggest Common Factor Method
Now, list down the factors of 2128
:1,2,4,7,8,14,16,19,28,38,56,76,112,133,152,266,304,532,1064,2128
Now, list down the factors of 9198
:1,2,3,6,7,9,14,18,21,42,63,73,126,146,219,438,511,657,1022,1314,1533,3066,4599,9198
Greatest Common Factor
We found the factors 2128,9198 . The biggest common factor number is the GCF number.
So the greatest common factor 2128,9198 is 14.
Lets's calculate LCM of 568,2214
| 2 | 568, 2214 |
| 284, 1107 |
∴ So the LCM of the given numbers is 2 x 284 x 1107 = 628776
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/628776
Therefore, the GCF of Fractions 2128/568,9198/2214 is 14/628776
Least Common Multiple of 568,2214 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 568,2214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(568,2214) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(568,2214) x common factors =2 x 1 = 2
LCM(568,2214) = ( 568 × 2214 ) / 2
LCM(568,2214) = 1257552 / 2
LCM(568,2214) = 628776
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FAQs on GCF of Fractions of 2128/568, 9198/2214
1. What is the HCF of 2128,9198?
The HCF of 2128,9198 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 2128/568, 9198/2214?
Answer: GCF of Numerators as per given numbers 2128/568, 9198/2214 is
GCF of Numerators i.e. for 2128,9198 is 14
LCM of denominators i.e. for 568,2214 is 628776.
Thus, GCF of Fractions is 14/628776.Finally, GCF of Fractions for 2128/568, 9198/2214 is 14/628776.