GCF of 7830/231, 1230/496
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7830/231, 1230/496 i.e 30/114576 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7830/231, 1230/496.
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 7830/231,1230/496?
Given fractions are 7830/231,1230/496
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 7830/231,1230/496, numerators are 7830,1230
Denominators are 231,496
The GCF of 7830,1230 is 30 .
LCM of 231,496 is 114576.
The greatest common factor of 7830/231,1230/496 = [GCF of 7830,1230]/[LCM of 231,496]= 30/114576
Therefore, the GCF of 7830/231,1230/496 is 30/114576.
To find the highest common factor of 7830,1230, we have to find the factors of both numbers and list the highest common factor.
The factors of 7830 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 27, 29, 30, 45, 54, 58, 87, 90, 135, 145, 174, 261, 270, 290, 435, 522, 783, 870, 1305, 1566, 2610, 3915, 7830
The factors of 1230 are 1, 2, 3, 5, 6, 10, 15, 30, 41, 82, 123, 205, 246, 410, 615, 1230
The HCF of 7830,1230 is 30.
Lets's calculate GCF of 7830,1230
| 2 | 7830, 1230 |
| 3 | 3915, 615 |
| 5 | 1305, 205 |
| 261, 41 |
∴ So the GCF of the given numbers is 2 x 3 x 5 = 30
Greatest Common Factor of 7830,1230 By Matching Biggest Common Factor Method
Now, list down the factors of 7830
:1,2,3,5,6,9,10,15,18,27,29,30,45,54,58,87,90,135,145,174,261,270,290,435,522,783,870,1305,1566,2610,3915,7830
Now, list down the factors of 1230
:1,2,3,5,6,10,15,30,41,82,123,205,246,410,615,1230
Greatest Common Factor
We found the factors 7830,1230 . The biggest common factor number is the GCF number.
So the greatest common factor 7830,1230 is 30.
Lets's calculate LCM of 231,496
Given numbers has no common factors except 1. So, there LCM is their product i.e 114576
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 30/114576
Therefore, the GCF of Fractions 7830/231,1230/496 is 30/114576
Least Common Multiple of 231,496 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 231,496 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(231,496) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(231,496) x common factors =1 x 1 = 1
LCM(231,496) = ( 231 × 496 ) / 1
LCM(231,496) = 114576 / 1
LCM(231,496) = 114576
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FAQs on GCF of Fractions of 7830/231, 1230/496
1. What is the HCF of 7830,1230?
The HCF of 7830,1230 is 30
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 7830/231, 1230/496?
Answer: GCF of Numerators as per given numbers 7830/231, 1230/496 is
GCF of Numerators i.e. for 7830,1230 is 30
LCM of denominators i.e. for 231,496 is 114576.
Thus, GCF of Fractions is 30/114576.Finally, GCF of Fractions for 7830/231, 1230/496 is 30/114576.