GCF of 7300/651, 8400/1152
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7300/651, 8400/1152 i.e 100/249984 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7300/651, 8400/1152.
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 7300/651,8400/1152?
Given fractions are 7300/651,8400/1152
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 7300/651,8400/1152, numerators are 7300,8400
Denominators are 651,1152
The GCF of 7300,8400 is 100 .
LCM of 651,1152 is 249984.
The greatest common factor of 7300/651,8400/1152 = [GCF of 7300,8400]/[LCM of 651,1152]= 100/249984
Therefore, the GCF of 7300/651,8400/1152 is 100/249984.
To find the highest common factor of 7300,8400, we have to find the factors of both numbers and list the highest common factor.
The factors of 7300 are 1, 2, 4, 5, 10, 20, 25, 50, 73, 100, 146, 292, 365, 730, 1460, 1825, 3650, 7300
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 7300,8400 is 100.
Lets's calculate GCF of 7300,8400
| 2 | 7300, 8400 |
| 2 | 3650, 4200 |
| 5 | 1825, 2100 |
| 5 | 365, 420 |
| 73, 84 |
∴ So the GCF of the given numbers is 2 x 2 x 5 x 5 = 100
Greatest Common Factor of 7300,8400 By Matching Biggest Common Factor Method
Now, list down the factors of 7300
:1,2,4,5,10,20,25,50,73,100,146,292,365,730,1460,1825,3650,7300
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 7300,8400 . The biggest common factor number is the GCF number.
So the greatest common factor 7300,8400 is 100.
Lets's calculate LCM of 651,1152
| 3 | 651, 1152 |
| 217, 384 |
∴ So the LCM of the given numbers is 3 x 217 x 384 = 249984
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 100/249984
Therefore, the GCF of Fractions 7300/651,8400/1152 is 100/249984
Least Common Multiple of 651,1152 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 651,1152 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(651,1152) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(651,1152) x common factors =3 x 1 = 3
LCM(651,1152) = ( 651 × 1152 ) / 3
LCM(651,1152) = 749952 / 3
LCM(651,1152) = 249984
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FAQs on GCF of Fractions of 7300/651, 8400/1152
1. What is the HCF of 7300,8400?
The HCF of 7300,8400 is 100
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 7300/651, 8400/1152?
Answer: GCF of Numerators as per given numbers 7300/651, 8400/1152 is
GCF of Numerators i.e. for 7300,8400 is 100
LCM of denominators i.e. for 651,1152 is 249984.
Thus, GCF of Fractions is 100/249984.Finally, GCF of Fractions for 7300/651, 8400/1152 is 100/249984.