GCF of 1210/414, 2920/5816
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1210/414, 2920/5816 i.e 10/1203912 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1210/414, 2920/5816.
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 1210/414,2920/5816?
Given fractions are 1210/414,2920/5816
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 1210/414,2920/5816, numerators are 1210,2920
Denominators are 414,5816
The GCF of 1210,2920 is 10 .
LCM of 414,5816 is 1203912.
The greatest common factor of 1210/414,2920/5816 = [GCF of 1210,2920]/[LCM of 414,5816]= 10/1203912
Therefore, the GCF of 1210/414,2920/5816 is 10/1203912.
To find the highest common factor of 1210,2920, we have to find the factors of both numbers and list the highest common factor.
The factors of 1210 are 1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605, 1210
The factors of 2920 are 1, 2, 4, 5, 8, 10, 20, 40, 73, 146, 292, 365, 584, 730, 1460, 2920
The HCF of 1210,2920 is 10.
Lets's calculate GCF of 1210,2920
| 2 | 1210, 2920 |
| 5 | 605, 1460 |
| 121, 292 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 1210,2920 By Matching Biggest Common Factor Method
Now, list down the factors of 1210
:1,2,5,10,11,22,55,110,121,242,605,1210
Now, list down the factors of 2920
:1,2,4,5,8,10,20,40,73,146,292,365,584,730,1460,2920
Greatest Common Factor
We found the factors 1210,2920 . The biggest common factor number is the GCF number.
So the greatest common factor 1210,2920 is 10.
Lets's calculate LCM of 414,5816
| 2 | 414, 5816 |
| 207, 2908 |
∴ So the LCM of the given numbers is 2 x 207 x 2908 = 1203912
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/1203912
Therefore, the GCF of Fractions 1210/414,2920/5816 is 10/1203912
Least Common Multiple of 414,5816 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 414,5816 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,5816) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(414,5816) x common factors =2 x 1 = 2
LCM(414,5816) = ( 414 × 5816 ) / 2
LCM(414,5816) = 2407824 / 2
LCM(414,5816) = 1203912
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FAQs on GCF of Fractions of 1210/414, 2920/5816
1. What is the HCF of 1210,2920?
The HCF of 1210,2920 is 10
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 1210/414, 2920/5816?
Answer: GCF of Numerators as per given numbers 1210/414, 2920/5816 is
GCF of Numerators i.e. for 1210,2920 is 10
LCM of denominators i.e. for 414,5816 is 1203912.
Thus, GCF of Fractions is 10/1203912.Finally, GCF of Fractions for 1210/414, 2920/5816 is 10/1203912.