GCF of 1740/172, 9102/7667
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1740/172, 9102/7667 i.e 6/1318724 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1740/172, 9102/7667.
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 1740/172,9102/7667?
Given fractions are 1740/172,9102/7667
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 1740/172,9102/7667, numerators are 1740,9102
Denominators are 172,7667
The GCF of 1740,9102 is 6 .
LCM of 172,7667 is 1318724.
The greatest common factor of 1740/172,9102/7667 = [GCF of 1740,9102]/[LCM of 172,7667]= 6/1318724
Therefore, the GCF of 1740/172,9102/7667 is 6/1318724.
To find the highest common factor of 1740,9102, we have to find the factors of both numbers and list the highest common factor.
The factors of 1740 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 29, 30, 58, 60, 87, 116, 145, 174, 290, 348, 435, 580, 870, 1740
The factors of 9102 are 1, 2, 3, 6, 37, 41, 74, 82, 111, 123, 222, 246, 1517, 3034, 4551, 9102
The HCF of 1740,9102 is 6.
Lets's calculate GCF of 1740,9102
| 2 | 1740, 9102 |
| 3 | 870, 4551 |
| 290, 1517 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 1740,9102 By Matching Biggest Common Factor Method
Now, list down the factors of 1740
:1,2,3,4,5,6,10,12,15,20,29,30,58,60,87,116,145,174,290,348,435,580,870,1740
Now, list down the factors of 9102
:1,2,3,6,37,41,74,82,111,123,222,246,1517,3034,4551,9102
Greatest Common Factor
We found the factors 1740,9102 . The biggest common factor number is the GCF number.
So the greatest common factor 1740,9102 is 6.
Lets's calculate LCM of 172,7667
Given numbers has no common factors except 1. So, there LCM is their product i.e 1318724
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/1318724
Therefore, the GCF of Fractions 1740/172,9102/7667 is 6/1318724
Least Common Multiple of 172,7667 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 172,7667 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(172,7667) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(172,7667) x common factors =1 x 1 = 1
LCM(172,7667) = ( 172 × 7667 ) / 1
LCM(172,7667) = 1318724 / 1
LCM(172,7667) = 1318724
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FAQs on GCF of Fractions of 1740/172, 9102/7667
1. What is the HCF of 1740,9102?
The HCF of 1740,9102 is 6
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 1740/172, 9102/7667?
Answer: GCF of Numerators as per given numbers 1740/172, 9102/7667 is
GCF of Numerators i.e. for 1740,9102 is 6
LCM of denominators i.e. for 172,7667 is 1318724.
Thus, GCF of Fractions is 6/1318724.Finally, GCF of Fractions for 1740/172, 9102/7667 is 6/1318724.