GCF of 1190/758, 1140/2106
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1190/758, 1140/2106 i.e 10/798174 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1190/758, 1140/2106.
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 1190/758,1140/2106?
Given fractions are 1190/758,1140/2106
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 1190/758,1140/2106, numerators are 1190,1140
Denominators are 758,2106
The GCF of 1190,1140 is 10 .
LCM of 758,2106 is 798174.
The greatest common factor of 1190/758,1140/2106 = [GCF of 1190,1140]/[LCM of 758,2106]= 10/798174
Therefore, the GCF of 1190/758,1140/2106 is 10/798174.
To find the highest common factor of 1190,1140, we have to find the factors of both numbers and list the highest common factor.
The factors of 1190 are 1, 2, 5, 7, 10, 14, 17, 34, 35, 70, 85, 119, 170, 238, 595, 1190
The factors of 1140 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 19, 20, 30, 38, 57, 60, 76, 95, 114, 190, 228, 285, 380, 570, 1140
The HCF of 1190,1140 is 10.
Lets's calculate GCF of 1190,1140
| 2 | 1190, 1140 |
| 5 | 595, 570 |
| 119, 114 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 1190,1140 By Matching Biggest Common Factor Method
Now, list down the factors of 1190
:1,2,5,7,10,14,17,34,35,70,85,119,170,238,595,1190
Now, list down the factors of 1140
:1,2,3,4,5,6,10,12,15,19,20,30,38,57,60,76,95,114,190,228,285,380,570,1140
Greatest Common Factor
We found the factors 1190,1140 . The biggest common factor number is the GCF number.
So the greatest common factor 1190,1140 is 10.
Lets's calculate LCM of 758,2106
| 2 | 758, 2106 |
| 379, 1053 |
∴ So the LCM of the given numbers is 2 x 379 x 1053 = 798174
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/798174
Therefore, the GCF of Fractions 1190/758,1140/2106 is 10/798174
Least Common Multiple of 758,2106 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 758,2106 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(758,2106) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(758,2106) x common factors =2 x 1 = 2
LCM(758,2106) = ( 758 × 2106 ) / 2
LCM(758,2106) = 1596348 / 2
LCM(758,2106) = 798174
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FAQs on GCF of Fractions of 1190/758, 1140/2106
1. What is the HCF of 1190,1140?
The HCF of 1190,1140 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 1190/758, 1140/2106?
Answer: GCF of Numerators as per given numbers 1190/758, 1140/2106 is
GCF of Numerators i.e. for 1190,1140 is 10
LCM of denominators i.e. for 758,2106 is 798174.
Thus, GCF of Fractions is 10/798174.Finally, GCF of Fractions for 1190/758, 1140/2106 is 10/798174.