GCF of 104/312, 9720/1455
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 104/312, 9720/1455 i.e 8/151320 easily. The following is the detailed procedure to determine the greatest common factor of fractions 104/312, 9720/1455.
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 104/312,9720/1455?
Given fractions are 104/312,9720/1455
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 104/312,9720/1455, numerators are 104,9720
Denominators are 312,1455
The GCF of 104,9720 is 8 .
LCM of 312,1455 is 151320.
The greatest common factor of 104/312,9720/1455 = [GCF of 104,9720]/[LCM of 312,1455]= 8/151320
Therefore, the GCF of 104/312,9720/1455 is 8/151320.
To find the highest common factor of 104,9720, we have to find the factors of both numbers and list the highest common factor.
The factors of 104 are 1, 2, 4, 8, 13, 26, 52, 104
The factors of 9720 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 81, 90, 108, 120, 135, 162, 180, 216, 243, 270, 324, 360, 405, 486, 540, 648, 810, 972, 1080, 1215, 1620, 1944, 2430, 3240, 4860, 9720
The HCF of 104,9720 is 8.
Lets's calculate GCF of 104,9720
| 2 | 104, 9720 |
| 2 | 52, 4860 |
| 2 | 26, 2430 |
| 13, 1215 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Greatest Common Factor of 104,9720 By Matching Biggest Common Factor Method
Now, list down the factors of 104
:1,2,4,8,13,26,52,104
Now, list down the factors of 9720
:1,2,3,4,5,6,8,9,10,12,15,18,20,24,27,30,36,40,45,54,60,72,81,90,108,120,135,162,180,216,243,270,324,360,405,486,540,648,810,972,1080,1215,1620,1944,2430,3240,4860,9720
Greatest Common Factor
We found the factors 104,9720 . The biggest common factor number is the GCF number.
So the greatest common factor 104,9720 is 8.
Lets's calculate LCM of 312,1455
| 3 | 312, 1455 |
| 104, 485 |
∴ So the LCM of the given numbers is 3 x 104 x 485 = 151320
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/151320
Therefore, the GCF of Fractions 104/312,9720/1455 is 8/151320
Least Common Multiple of 312,1455 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 312,1455 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(312,1455) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(312,1455) x common factors =3 x 1 = 3
LCM(312,1455) = ( 312 × 1455 ) / 3
LCM(312,1455) = 453960 / 3
LCM(312,1455) = 151320
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FAQs on GCF of Fractions of 104/312, 9720/1455
1. What is the HCF of 104,9720?
The HCF of 104,9720 is 8
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 104/312, 9720/1455?
Answer: GCF of Numerators as per given numbers 104/312, 9720/1455 is
GCF of Numerators i.e. for 104,9720 is 8
LCM of denominators i.e. for 312,1455 is 151320.
Thus, GCF of Fractions is 8/151320.Finally, GCF of Fractions for 104/312, 9720/1455 is 8/151320.