GCF of 1830/106, 7142/570
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1830/106, 7142/570 i.e 2/30210 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1830/106, 7142/570.
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 1830/106,7142/570?
Given fractions are 1830/106,7142/570
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 1830/106,7142/570, numerators are 1830,7142
Denominators are 106,570
The GCF of 1830,7142 is 2 .
LCM of 106,570 is 30210.
The greatest common factor of 1830/106,7142/570 = [GCF of 1830,7142]/[LCM of 106,570]= 2/30210
Therefore, the GCF of 1830/106,7142/570 is 2/30210.
To find the highest common factor of 1830,7142, we have to find the factors of both numbers and list the highest common factor.
The factors of 1830 are 1, 2, 3, 5, 6, 10, 15, 30, 61, 122, 183, 305, 366, 610, 915, 1830
The factors of 7142 are 1, 2, 3571, 7142
The HCF of 1830,7142 is 2.
Lets's calculate GCF of 1830,7142
| 2 | 1830, 7142 |
| 915, 3571 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 1830,7142 By Matching Biggest Common Factor Method
Now, list down the factors of 1830
:1,2,3,5,6,10,15,30,61,122,183,305,366,610,915,1830
Now, list down the factors of 7142
:1,2,3571,7142
Greatest Common Factor
We found the factors 1830,7142 . The biggest common factor number is the GCF number.
So the greatest common factor 1830,7142 is 2.
Lets's calculate LCM of 106,570
| 2 | 106, 570 |
| 53, 285 |
∴ So the LCM of the given numbers is 2 x 53 x 285 = 30210
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/30210
Therefore, the GCF of Fractions 1830/106,7142/570 is 2/30210
Least Common Multiple of 106,570 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 106,570 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(106,570) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(106,570) x common factors =2 x 1 = 2
LCM(106,570) = ( 106 × 570 ) / 2
LCM(106,570) = 60420 / 2
LCM(106,570) = 30210
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FAQs on GCF of Fractions of 1830/106, 7142/570
1. What is the HCF of 1830,7142?
The HCF of 1830,7142 is 2
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 1830/106, 7142/570?
Answer: GCF of Numerators as per given numbers 1830/106, 7142/570 is
GCF of Numerators i.e. for 1830,7142 is 2
LCM of denominators i.e. for 106,570 is 30210.
Thus, GCF of Fractions is 2/30210.Finally, GCF of Fractions for 1830/106, 7142/570 is 2/30210.