GCF of 185/378, 7920/1233
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 185/378, 7920/1233 i.e 5/51786 easily. The following is the detailed procedure to determine the greatest common factor of fractions 185/378, 7920/1233.
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 185/378,7920/1233?
Given fractions are 185/378,7920/1233
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 185/378,7920/1233, numerators are 185,7920
Denominators are 378,1233
The GCF of 185,7920 is 5 .
LCM of 378,1233 is 51786.
The greatest common factor of 185/378,7920/1233 = [GCF of 185,7920]/[LCM of 378,1233]= 5/51786
Therefore, the GCF of 185/378,7920/1233 is 5/51786.
To find the highest common factor of 185,7920, we have to find the factors of both numbers and list the highest common factor.
The factors of 185 are 1, 5, 37, 185
The factors of 7920 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 15, 16, 18, 20, 22, 24, 30, 33, 36, 40, 44, 45, 48, 55, 60, 66, 72, 80, 88, 90, 99, 110, 120, 132, 144, 165, 176, 180, 198, 220, 240, 264, 330, 360, 396, 440, 495, 528, 660, 720, 792, 880, 990, 1320, 1584, 1980, 2640, 3960, 7920
The HCF of 185,7920 is 5.
Lets's calculate GCF of 185,7920
| 5 | 185, 7920 |
| 37, 1584 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 185,7920 By Matching Biggest Common Factor Method
Now, list down the factors of 185
:1,5,37,185
Now, list down the factors of 7920
:1,2,3,4,5,6,8,9,10,11,12,15,16,18,20,22,24,30,33,36,40,44,45,48,55,60,66,72,80,88,90,99,110,120,132,144,165,176,180,198,220,240,264,330,360,396,440,495,528,660,720,792,880,990,1320,1584,1980,2640,3960,7920
Greatest Common Factor
We found the factors 185,7920 . The biggest common factor number is the GCF number.
So the greatest common factor 185,7920 is 5.
Lets's calculate LCM of 378,1233
| 3 | 378, 1233 |
| 3 | 126, 411 |
| 42, 137 |
∴ So the LCM of the given numbers is 3 x 3 x 42 x 137 = 51786
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/51786
Therefore, the GCF of Fractions 185/378,7920/1233 is 5/51786
Least Common Multiple of 378,1233 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 378,1233 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(378,1233) = 9
common factors(in case of two or more numbers have common factors) = 1
GCF(378,1233) x common factors =9 x 1 = 9
LCM(378,1233) = ( 378 × 1233 ) / 9
LCM(378,1233) = 466074 / 9
LCM(378,1233) = 51786
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 185/378, 7920/1233
1. What is the HCF of 185,7920?
The HCF of 185,7920 is 5
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 185/378, 7920/1233?
Answer: GCF of Numerators as per given numbers 185/378, 7920/1233 is
GCF of Numerators i.e. for 185,7920 is 5
LCM of denominators i.e. for 378,1233 is 51786.
Thus, GCF of Fractions is 5/51786.Finally, GCF of Fractions for 185/378, 7920/1233 is 5/51786.