GCF of 1518/408, 7524/2744
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1518/408, 7524/2744 i.e 66/139944 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1518/408, 7524/2744.
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 1518/408,7524/2744?
Given fractions are 1518/408,7524/2744
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 1518/408,7524/2744, numerators are 1518,7524
Denominators are 408,2744
The GCF of 1518,7524 is 66 .
LCM of 408,2744 is 139944.
The greatest common factor of 1518/408,7524/2744 = [GCF of 1518,7524]/[LCM of 408,2744]= 66/139944
Therefore, the GCF of 1518/408,7524/2744 is 66/139944.
To find the highest common factor of 1518,7524, we have to find the factors of both numbers and list the highest common factor.
The factors of 1518 are 1, 2, 3, 6, 11, 22, 23, 33, 46, 66, 69, 138, 253, 506, 759, 1518
The factors of 7524 are 1, 2, 3, 4, 6, 9, 11, 12, 18, 19, 22, 33, 36, 38, 44, 57, 66, 76, 99, 114, 132, 171, 198, 209, 228, 342, 396, 418, 627, 684, 836, 1254, 1881, 2508, 3762, 7524
The HCF of 1518,7524 is 66.
Lets's calculate GCF of 1518,7524
| 2 | 1518, 7524 |
| 3 | 759, 3762 |
| 11 | 253, 1254 |
| 23, 114 |
∴ So the GCF of the given numbers is 2 x 3 x 11 = 66
Greatest Common Factor of 1518,7524 By Matching Biggest Common Factor Method
Now, list down the factors of 1518
:1,2,3,6,11,22,23,33,46,66,69,138,253,506,759,1518
Now, list down the factors of 7524
:1,2,3,4,6,9,11,12,18,19,22,33,36,38,44,57,66,76,99,114,132,171,198,209,228,342,396,418,627,684,836,1254,1881,2508,3762,7524
Greatest Common Factor
We found the factors 1518,7524 . The biggest common factor number is the GCF number.
So the greatest common factor 1518,7524 is 66.
Lets's calculate LCM of 408,2744
| 2 | 408, 2744 |
| 2 | 204, 1372 |
| 2 | 102, 686 |
| 51, 343 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 51 x 343 = 139944
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 66/139944
Therefore, the GCF of Fractions 1518/408,7524/2744 is 66/139944
Least Common Multiple of 408,2744 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 408,2744 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(408,2744) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(408,2744) x common factors =8 x 1 = 8
LCM(408,2744) = ( 408 × 2744 ) / 8
LCM(408,2744) = 1119552 / 8
LCM(408,2744) = 139944
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 1518/408, 7524/2744
1. What is the HCF of 1518,7524?
The HCF of 1518,7524 is 66
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 1518/408, 7524/2744?
Answer: GCF of Numerators as per given numbers 1518/408, 7524/2744 is
GCF of Numerators i.e. for 1518,7524 is 66
LCM of denominators i.e. for 408,2744 is 139944.
Thus, GCF of Fractions is 66/139944.Finally, GCF of Fractions for 1518/408, 7524/2744 is 66/139944.