GCF of 1234/414, 5184/7518
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1234/414, 5184/7518 i.e 2/518742 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1234/414, 5184/7518.
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 1234/414,5184/7518?
Given fractions are 1234/414,5184/7518
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 1234/414,5184/7518, numerators are 1234,5184
Denominators are 414,7518
The GCF of 1234,5184 is 2 .
LCM of 414,7518 is 518742.
The greatest common factor of 1234/414,5184/7518 = [GCF of 1234,5184]/[LCM of 414,7518]= 2/518742
Therefore, the GCF of 1234/414,5184/7518 is 2/518742.
To find the highest common factor of 1234,5184, we have to find the factors of both numbers and list the highest common factor.
The factors of 1234 are 1, 2, 617, 1234
The factors of 5184 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 81, 96, 108, 144, 162, 192, 216, 288, 324, 432, 576, 648, 864, 1296, 1728, 2592, 5184
The HCF of 1234,5184 is 2.
Lets's calculate GCF of 1234,5184
| 2 | 1234, 5184 |
| 617, 2592 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1234,5184 By Matching Biggest Common Factor Method
Now, list down the factors of 1234
:1,2,617,1234
Now, list down the factors of 5184
:1,2,3,4,6,8,9,12,16,18,24,27,32,36,48,54,64,72,81,96,108,144,162,192,216,288,324,432,576,648,864,1296,1728,2592,5184
Greatest Common Factor
We found the factors 1234,5184 . The biggest common factor number is the GCF number.
So the greatest common factor 1234,5184 is 2.
Lets's calculate LCM of 414,7518
| 2 | 414, 7518 |
| 3 | 207, 3759 |
| 69, 1253 |
∴ So the LCM of the given numbers is 2 x 3 x 69 x 1253 = 518742
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/518742
Therefore, the GCF of Fractions 1234/414,5184/7518 is 2/518742
Least Common Multiple of 414,7518 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 414,7518 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,7518) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(414,7518) x common factors =6 x 1 = 6
LCM(414,7518) = ( 414 × 7518 ) / 6
LCM(414,7518) = 3112452 / 6
LCM(414,7518) = 518742
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FAQs on GCF of Fractions of 1234/414, 5184/7518
1. What is the HCF of 1234,5184?
The HCF of 1234,5184 is 2
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 1234/414, 5184/7518?
Answer: GCF of Numerators as per given numbers 1234/414, 5184/7518 is
GCF of Numerators i.e. for 1234,5184 is 2
LCM of denominators i.e. for 414,7518 is 518742.
Thus, GCF of Fractions is 2/518742.Finally, GCF of Fractions for 1234/414, 5184/7518 is 2/518742.