GCF of 1806/782, 4760/7514
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1806/782, 4760/7514 i.e 14/172822 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1806/782, 4760/7514.
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 1806/782,4760/7514?
Given fractions are 1806/782,4760/7514
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 1806/782,4760/7514, numerators are 1806,4760
Denominators are 782,7514
The GCF of 1806,4760 is 14 .
LCM of 782,7514 is 172822.
The greatest common factor of 1806/782,4760/7514 = [GCF of 1806,4760]/[LCM of 782,7514]= 14/172822
Therefore, the GCF of 1806/782,4760/7514 is 14/172822.
To find the highest common factor of 1806,4760, we have to find the factors of both numbers and list the highest common factor.
The factors of 1806 are 1, 2, 3, 6, 7, 14, 21, 42, 43, 86, 129, 258, 301, 602, 903, 1806
The factors of 4760 are 1, 2, 4, 5, 7, 8, 10, 14, 17, 20, 28, 34, 35, 40, 56, 68, 70, 85, 119, 136, 140, 170, 238, 280, 340, 476, 595, 680, 952, 1190, 2380, 4760
The HCF of 1806,4760 is 14.
Lets's calculate GCF of 1806,4760
| 2 | 1806, 4760 |
| 7 | 903, 2380 |
| 129, 340 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 1806,4760 By Matching Biggest Common Factor Method
Now, list down the factors of 1806
:1,2,3,6,7,14,21,42,43,86,129,258,301,602,903,1806
Now, list down the factors of 4760
:1,2,4,5,7,8,10,14,17,20,28,34,35,40,56,68,70,85,119,136,140,170,238,280,340,476,595,680,952,1190,2380,4760
Greatest Common Factor
We found the factors 1806,4760 . The biggest common factor number is the GCF number.
So the greatest common factor 1806,4760 is 14.
Lets's calculate LCM of 782,7514
| 2 | 782, 7514 |
| 17 | 391, 3757 |
| 23, 221 |
∴ So the LCM of the given numbers is 2 x 17 x 23 x 221 = 172822
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/172822
Therefore, the GCF of Fractions 1806/782,4760/7514 is 14/172822
Least Common Multiple of 782,7514 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 782,7514 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(782,7514) = 34
common factors(in case of two or more numbers have common factors) = 1
GCF(782,7514) x common factors =34 x 1 = 34
LCM(782,7514) = ( 782 × 7514 ) / 34
LCM(782,7514) = 5875948 / 34
LCM(782,7514) = 172822
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 1806/782, 4760/7514
1. What is the HCF of 1806,4760?
The HCF of 1806,4760 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 1806/782, 4760/7514?
Answer: GCF of Numerators as per given numbers 1806/782, 4760/7514 is
GCF of Numerators i.e. for 1806,4760 is 14
LCM of denominators i.e. for 782,7514 is 172822.
Thus, GCF of Fractions is 14/172822.Finally, GCF of Fractions for 1806/782, 4760/7514 is 14/172822.