GCF of 7406/140, 7750/3192
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7406/140, 7750/3192 i.e 2/15960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7406/140, 7750/3192.
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 7406/140,7750/3192?
Given fractions are 7406/140,7750/3192
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 7406/140,7750/3192, numerators are 7406,7750
Denominators are 140,3192
The GCF of 7406,7750 is 2 .
LCM of 140,3192 is 15960.
The greatest common factor of 7406/140,7750/3192 = [GCF of 7406,7750]/[LCM of 140,3192]= 2/15960
Therefore, the GCF of 7406/140,7750/3192 is 2/15960.
To find the highest common factor of 7406,7750, we have to find the factors of both numbers and list the highest common factor.
The factors of 7406 are 1, 2, 7, 14, 23, 46, 161, 322, 529, 1058, 3703, 7406
The factors of 7750 are 1, 2, 5, 10, 25, 31, 50, 62, 125, 155, 250, 310, 775, 1550, 3875, 7750
The HCF of 7406,7750 is 2.
Lets's calculate GCF of 7406,7750
| 2 | 7406, 7750 |
| 3703, 3875 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 7406,7750 By Matching Biggest Common Factor Method
Now, list down the factors of 7406
:1,2,7,14,23,46,161,322,529,1058,3703,7406
Now, list down the factors of 7750
:1,2,5,10,25,31,50,62,125,155,250,310,775,1550,3875,7750
Greatest Common Factor
We found the factors 7406,7750 . The biggest common factor number is the GCF number.
So the greatest common factor 7406,7750 is 2.
Lets's calculate LCM of 140,3192
| 2 | 140, 3192 |
| 2 | 70, 1596 |
| 7 | 35, 798 |
| 5, 114 |
∴ So the LCM of the given numbers is 2 x 2 x 7 x 5 x 114 = 15960
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/15960
Therefore, the GCF of Fractions 7406/140,7750/3192 is 2/15960
Least Common Multiple of 140,3192 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 140,3192 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(140,3192) = 28
common factors(in case of two or more numbers have common factors) = 1
GCF(140,3192) x common factors =28 x 1 = 28
LCM(140,3192) = ( 140 × 3192 ) / 28
LCM(140,3192) = 446880 / 28
LCM(140,3192) = 15960
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 7406/140, 7750/3192
1. What is the HCF of 7406,7750?
The HCF of 7406,7750 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 7406/140, 7750/3192?
Answer: GCF of Numerators as per given numbers 7406/140, 7750/3192 is
GCF of Numerators i.e. for 7406,7750 is 2
LCM of denominators i.e. for 140,3192 is 15960.
Thus, GCF of Fractions is 2/15960.Finally, GCF of Fractions for 7406/140, 7750/3192 is 2/15960.