GCF of 2960/354, 7830/1860
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2960/354, 7830/1860 i.e 10/109740 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2960/354, 7830/1860.
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 2960/354,7830/1860?
Given fractions are 2960/354,7830/1860
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 2960/354,7830/1860, numerators are 2960,7830
Denominators are 354,1860
The GCF of 2960,7830 is 10 .
LCM of 354,1860 is 109740.
The greatest common factor of 2960/354,7830/1860 = [GCF of 2960,7830]/[LCM of 354,1860]= 10/109740
Therefore, the GCF of 2960/354,7830/1860 is 10/109740.
To find the highest common factor of 2960,7830, we have to find the factors of both numbers and list the highest common factor.
The factors of 2960 are 1, 2, 4, 5, 8, 10, 16, 20, 37, 40, 74, 80, 148, 185, 296, 370, 592, 740, 1480, 2960
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 HCF of 2960,7830 is 10.
Lets's calculate GCF of 2960,7830
| 2 | 2960, 7830 |
| 5 | 1480, 3915 |
| 296, 783 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 2960,7830 By Matching Biggest Common Factor Method
Now, list down the factors of 2960
:1,2,4,5,8,10,16,20,37,40,74,80,148,185,296,370,592,740,1480,2960
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
Greatest Common Factor
We found the factors 2960,7830 . The biggest common factor number is the GCF number.
So the greatest common factor 2960,7830 is 10.
Lets's calculate LCM of 354,1860
| 2 | 354, 1860 |
| 3 | 177, 930 |
| 59, 310 |
∴ So the LCM of the given numbers is 2 x 3 x 59 x 310 = 109740
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/109740
Therefore, the GCF of Fractions 2960/354,7830/1860 is 10/109740
Least Common Multiple of 354,1860 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 354,1860 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(354,1860) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(354,1860) x common factors =6 x 1 = 6
LCM(354,1860) = ( 354 × 1860 ) / 6
LCM(354,1860) = 658440 / 6
LCM(354,1860) = 109740
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FAQs on GCF of Fractions of 2960/354, 7830/1860
1. What is the HCF of 2960,7830?
The HCF of 2960,7830 is 10
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 2960/354, 7830/1860?
Answer: GCF of Numerators as per given numbers 2960/354, 7830/1860 is
GCF of Numerators i.e. for 2960,7830 is 10
LCM of denominators i.e. for 354,1860 is 109740.
Thus, GCF of Fractions is 10/109740.Finally, GCF of Fractions for 2960/354, 7830/1860 is 10/109740.