GCF of 1428/459, 3519/230
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1428/459, 3519/230 i.e 51/105570 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1428/459, 3519/230.
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 1428/459,3519/230?
Given fractions are 1428/459,3519/230
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 1428/459,3519/230, numerators are 1428,3519
Denominators are 459,230
The GCF of 1428,3519 is 51 .
LCM of 459,230 is 105570.
The greatest common factor of 1428/459,3519/230 = [GCF of 1428,3519]/[LCM of 459,230]= 51/105570
Therefore, the GCF of 1428/459,3519/230 is 51/105570.
To find the highest common factor of 1428,3519, we have to find the factors of both numbers and list the highest common factor.
The factors of 1428 are 1, 2, 3, 4, 6, 7, 12, 14, 17, 21, 28, 34, 42, 51, 68, 84, 102, 119, 204, 238, 357, 476, 714, 1428
The factors of 3519 are 1, 3, 9, 17, 23, 51, 69, 153, 207, 391, 1173, 3519
The HCF of 1428,3519 is 51.
Lets's calculate GCF of 1428,3519
| 3 | 1428, 3519 |
| 17 | 476, 1173 |
| 28, 69 |
∴ So the GCF of the given numbers is 3 x 17 = 51
Greatest Common Factor of 1428,3519 By Matching Biggest Common Factor Method
Now, list down the factors of 1428
:1,2,3,4,6,7,12,14,17,21,28,34,42,51,68,84,102,119,204,238,357,476,714,1428
Now, list down the factors of 3519
:1,3,9,17,23,51,69,153,207,391,1173,3519
Greatest Common Factor
We found the factors 1428,3519 . The biggest common factor number is the GCF number.
So the greatest common factor 1428,3519 is 51.
Lets's calculate LCM of 459,230
Given numbers has no common factors except 1. So, there LCM is their product i.e 105570
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 51/105570
Therefore, the GCF of Fractions 1428/459,3519/230 is 51/105570
Least Common Multiple of 459,230 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 459,230 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(459,230) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(459,230) x common factors =1 x 1 = 1
LCM(459,230) = ( 459 × 230 ) / 1
LCM(459,230) = 105570 / 1
LCM(459,230) = 105570
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FAQs on GCF of Fractions of 1428/459, 3519/230
1. What is the HCF of 1428,3519?
The HCF of 1428,3519 is 51
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 1428/459, 3519/230?
Answer: GCF of Numerators as per given numbers 1428/459, 3519/230 is
GCF of Numerators i.e. for 1428,3519 is 51
LCM of denominators i.e. for 459,230 is 105570.
Thus, GCF of Fractions is 51/105570.Finally, GCF of Fractions for 1428/459, 3519/230 is 51/105570.