GCF of 9480/366, 8400/1006
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 9480/366, 8400/1006 i.e 120/184098 easily. The following is the detailed procedure to determine the greatest common factor of fractions 9480/366, 8400/1006.
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 9480/366,8400/1006?
Given fractions are 9480/366,8400/1006
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 9480/366,8400/1006, numerators are 9480,8400
Denominators are 366,1006
The GCF of 9480,8400 is 120 .
LCM of 366,1006 is 184098.
The greatest common factor of 9480/366,8400/1006 = [GCF of 9480,8400]/[LCM of 366,1006]= 120/184098
Therefore, the GCF of 9480/366,8400/1006 is 120/184098.
To find the highest common factor of 9480,8400, we have to find the factors of both numbers and list the highest common factor.
The factors of 9480 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 79, 120, 158, 237, 316, 395, 474, 632, 790, 948, 1185, 1580, 1896, 2370, 3160, 4740, 9480
The factors of 8400 are 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 16, 20, 21, 24, 25, 28, 30, 35, 40, 42, 48, 50, 56, 60, 70, 75, 80, 84, 100, 105, 112, 120, 140, 150, 168, 175, 200, 210, 240, 280, 300, 336, 350, 400, 420, 525, 560, 600, 700, 840, 1050, 1200, 1400, 1680, 2100, 2800, 4200, 8400
The HCF of 9480,8400 is 120.
Lets's calculate GCF of 9480,8400
| 2 | 9480, 8400 |
| 2 | 4740, 4200 |
| 2 | 2370, 2100 |
| 3 | 1185, 1050 |
| 5 | 395, 350 |
| 79, 70 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 x 5 = 120
Greatest Common Factor of 9480,8400 By Matching Biggest Common Factor Method
Now, list down the factors of 9480
:1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,79,120,158,237,316,395,474,632,790,948,1185,1580,1896,2370,3160,4740,9480
Now, list down the factors of 8400
:1,2,3,4,5,6,7,8,10,12,14,15,16,20,21,24,25,28,30,35,40,42,48,50,56,60,70,75,80,84,100,105,112,120,140,150,168,175,200,210,240,280,300,336,350,400,420,525,560,600,700,840,1050,1200,1400,1680,2100,2800,4200,8400
Greatest Common Factor
We found the factors 9480,8400 . The biggest common factor number is the GCF number.
So the greatest common factor 9480,8400 is 120.
Lets's calculate LCM of 366,1006
| 2 | 366, 1006 |
| 183, 503 |
∴ So the LCM of the given numbers is 2 x 183 x 503 = 184098
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 120/184098
Therefore, the GCF of Fractions 9480/366,8400/1006 is 120/184098
Least Common Multiple of 366,1006 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 366,1006 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(366,1006) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(366,1006) x common factors =2 x 1 = 2
LCM(366,1006) = ( 366 × 1006 ) / 2
LCM(366,1006) = 368196 / 2
LCM(366,1006) = 184098
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FAQs on GCF of Fractions of 9480/366, 8400/1006
1. What is the HCF of 9480,8400?
The HCF of 9480,8400 is 120
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 9480/366, 8400/1006?
Answer: GCF of Numerators as per given numbers 9480/366, 8400/1006 is
GCF of Numerators i.e. for 9480,8400 is 120
LCM of denominators i.e. for 366,1006 is 184098.
Thus, GCF of Fractions is 120/184098.Finally, GCF of Fractions for 9480/366, 8400/1006 is 120/184098.