GCF of 2114/493, 2198/2577
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2114/493, 2198/2577 i.e 14/1270461 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2114/493, 2198/2577.
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 2114/493,2198/2577?
Given fractions are 2114/493,2198/2577
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 2114/493,2198/2577, numerators are 2114,2198
Denominators are 493,2577
The GCF of 2114,2198 is 14 .
LCM of 493,2577 is 1270461.
The greatest common factor of 2114/493,2198/2577 = [GCF of 2114,2198]/[LCM of 493,2577]= 14/1270461
Therefore, the GCF of 2114/493,2198/2577 is 14/1270461.
To find the highest common factor of 2114,2198, we have to find the factors of both numbers and list the highest common factor.
The factors of 2114 are 1, 2, 7, 14, 151, 302, 1057, 2114
The factors of 2198 are 1, 2, 7, 14, 157, 314, 1099, 2198
The HCF of 2114,2198 is 14.
Lets's calculate GCF of 2114,2198
| 2 | 2114, 2198 |
| 7 | 1057, 1099 |
| 151, 157 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 2114,2198 By Matching Biggest Common Factor Method
Now, list down the factors of 2114
:1,2,7,14,151,302,1057,2114
Now, list down the factors of 2198
:1,2,7,14,157,314,1099,2198
Greatest Common Factor
We found the factors 2114,2198 . The biggest common factor number is the GCF number.
So the greatest common factor 2114,2198 is 14.
Lets's calculate LCM of 493,2577
Given numbers has no common factors except 1. So, there LCM is their product i.e 1270461
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/1270461
Therefore, the GCF of Fractions 2114/493,2198/2577 is 14/1270461
Least Common Multiple of 493,2577 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 493,2577 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(493,2577) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(493,2577) x common factors =1 x 1 = 1
LCM(493,2577) = ( 493 × 2577 ) / 1
LCM(493,2577) = 1270461 / 1
LCM(493,2577) = 1270461
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FAQs on GCF of Fractions of 2114/493, 2198/2577
1. What is the HCF of 2114,2198?
The HCF of 2114,2198 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 2114/493, 2198/2577?
Answer: GCF of Numerators as per given numbers 2114/493, 2198/2577 is
GCF of Numerators i.e. for 2114,2198 is 14
LCM of denominators i.e. for 493,2577 is 1270461.
Thus, GCF of Fractions is 14/1270461.Finally, GCF of Fractions for 2114/493, 2198/2577 is 14/1270461.