GCF of 1200/831, 7104/516
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1200/831, 7104/516 i.e 48/142932 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1200/831, 7104/516.
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 1200/831,7104/516?
Given fractions are 1200/831,7104/516
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 1200/831,7104/516, numerators are 1200,7104
Denominators are 831,516
The GCF of 1200,7104 is 48 .
LCM of 831,516 is 142932.
The greatest common factor of 1200/831,7104/516 = [GCF of 1200,7104]/[LCM of 831,516]= 48/142932
Therefore, the GCF of 1200/831,7104/516 is 48/142932.
To find the highest common factor of 1200,7104, we have to find the factors of both numbers and list the highest common factor.
The factors of 1200 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200
The factors of 7104 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 37, 48, 64, 74, 96, 111, 148, 192, 222, 296, 444, 592, 888, 1184, 1776, 2368, 3552, 7104
The HCF of 1200,7104 is 48.
Lets's calculate GCF of 1200,7104
| 2 | 1200, 7104 |
| 2 | 600, 3552 |
| 2 | 300, 1776 |
| 2 | 150, 888 |
| 3 | 75, 444 |
| 25, 148 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 2 x 3 = 48
Greatest Common Factor of 1200,7104 By Matching Biggest Common Factor Method
Now, list down the factors of 1200
:1,2,3,4,5,6,8,10,12,15,16,20,24,25,30,40,48,50,60,75,80,100,120,150,200,240,300,400,600,1200
Now, list down the factors of 7104
:1,2,3,4,6,8,12,16,24,32,37,48,64,74,96,111,148,192,222,296,444,592,888,1184,1776,2368,3552,7104
Greatest Common Factor
We found the factors 1200,7104 . The biggest common factor number is the GCF number.
So the greatest common factor 1200,7104 is 48.
Lets's calculate LCM of 831,516
| 3 | 831, 516 |
| 277, 172 |
∴ So the LCM of the given numbers is 3 x 277 x 172 = 142932
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 48/142932
Therefore, the GCF of Fractions 1200/831,7104/516 is 48/142932
Least Common Multiple of 831,516 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 831,516 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(831,516) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(831,516) x common factors =3 x 1 = 3
LCM(831,516) = ( 831 × 516 ) / 3
LCM(831,516) = 428796 / 3
LCM(831,516) = 142932
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FAQs on GCF of Fractions of 1200/831, 7104/516
1. What is the HCF of 1200,7104?
The HCF of 1200,7104 is 48
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 1200/831, 7104/516?
Answer: GCF of Numerators as per given numbers 1200/831, 7104/516 is
GCF of Numerators i.e. for 1200,7104 is 48
LCM of denominators i.e. for 831,516 is 142932.
Thus, GCF of Fractions is 48/142932.Finally, GCF of Fractions for 1200/831, 7104/516 is 48/142932.