GCF of 7809/176, 9750/4112
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7809/176, 9750/4112 i.e 3/45232 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7809/176, 9750/4112.
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 7809/176,9750/4112?
Given fractions are 7809/176,9750/4112
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 7809/176,9750/4112, numerators are 7809,9750
Denominators are 176,4112
The GCF of 7809,9750 is 3 .
LCM of 176,4112 is 45232.
The greatest common factor of 7809/176,9750/4112 = [GCF of 7809,9750]/[LCM of 176,4112]= 3/45232
Therefore, the GCF of 7809/176,9750/4112 is 3/45232.
To find the highest common factor of 7809,9750, we have to find the factors of both numbers and list the highest common factor.
The factors of 7809 are 1, 3, 19, 57, 137, 411, 2603, 7809
The factors of 9750 are 1, 2, 3, 5, 6, 10, 13, 15, 25, 26, 30, 39, 50, 65, 75, 78, 125, 130, 150, 195, 250, 325, 375, 390, 650, 750, 975, 1625, 1950, 3250, 4875, 9750
The HCF of 7809,9750 is 3.
Lets's calculate GCF of 7809,9750
| 3 | 7809, 9750 |
| 2603, 3250 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 7809,9750 By Matching Biggest Common Factor Method
Now, list down the factors of 7809
:1,3,19,57,137,411,2603,7809
Now, list down the factors of 9750
:1,2,3,5,6,10,13,15,25,26,30,39,50,65,75,78,125,130,150,195,250,325,375,390,650,750,975,1625,1950,3250,4875,9750
Greatest Common Factor
We found the factors 7809,9750 . The biggest common factor number is the GCF number.
So the greatest common factor 7809,9750 is 3.
Lets's calculate LCM of 176,4112
| 2 | 176, 4112 |
| 2 | 88, 2056 |
| 2 | 44, 1028 |
| 2 | 22, 514 |
| 11, 257 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 11 x 257 = 45232
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/45232
Therefore, the GCF of Fractions 7809/176,9750/4112 is 3/45232
Least Common Multiple of 176,4112 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 176,4112 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(176,4112) = 16
common factors(in case of two or more numbers have common factors) = 1
GCF(176,4112) x common factors =16 x 1 = 16
LCM(176,4112) = ( 176 × 4112 ) / 16
LCM(176,4112) = 723712 / 16
LCM(176,4112) = 45232
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FAQs on GCF of Fractions of 7809/176, 9750/4112
1. What is the HCF of 7809,9750?
The HCF of 7809,9750 is 3
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 7809/176, 9750/4112?
Answer: GCF of Numerators as per given numbers 7809/176, 9750/4112 is
GCF of Numerators i.e. for 7809,9750 is 3
LCM of denominators i.e. for 176,4112 is 45232.
Thus, GCF of Fractions is 3/45232.Finally, GCF of Fractions for 7809/176, 9750/4112 is 3/45232.