GCF of 900/324, 5208/214
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 900/324, 5208/214 i.e 12/34668 easily. The following is the detailed procedure to determine the greatest common factor of fractions 900/324, 5208/214.
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 900/324,5208/214?
Given fractions are 900/324,5208/214
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 900/324,5208/214, numerators are 900,5208
Denominators are 324,214
The GCF of 900,5208 is 12 .
LCM of 324,214 is 34668.
The greatest common factor of 900/324,5208/214 = [GCF of 900,5208]/[LCM of 324,214]= 12/34668
Therefore, the GCF of 900/324,5208/214 is 12/34668.
To find the highest common factor of 900,5208, we have to find the factors of both numbers and list the highest common factor.
The factors of 900 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 25, 30, 36, 45, 50, 60, 75, 90, 100, 150, 180, 225, 300, 450, 900
The factors of 5208 are 1, 2, 3, 4, 6, 7, 8, 12, 14, 21, 24, 28, 31, 42, 56, 62, 84, 93, 124, 168, 186, 217, 248, 372, 434, 651, 744, 868, 1302, 1736, 2604, 5208
The HCF of 900,5208 is 12.
Lets's calculate GCF of 900,5208
| 2 | 900, 5208 |
| 2 | 450, 2604 |
| 3 | 225, 1302 |
| 75, 434 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 900,5208 By Matching Biggest Common Factor Method
Now, list down the factors of 900
:1,2,3,4,5,6,9,10,12,15,18,20,25,30,36,45,50,60,75,90,100,150,180,225,300,450,900
Now, list down the factors of 5208
:1,2,3,4,6,7,8,12,14,21,24,28,31,42,56,62,84,93,124,168,186,217,248,372,434,651,744,868,1302,1736,2604,5208
Greatest Common Factor
We found the factors 900,5208 . The biggest common factor number is the GCF number.
So the greatest common factor 900,5208 is 12.
Lets's calculate LCM of 324,214
| 2 | 324, 214 |
| 162, 107 |
∴ So the LCM of the given numbers is 2 x 162 x 107 = 34668
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/34668
Therefore, the GCF of Fractions 900/324,5208/214 is 12/34668
Least Common Multiple of 324,214 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 324,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(324,214) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(324,214) x common factors =2 x 1 = 2
LCM(324,214) = ( 324 × 214 ) / 2
LCM(324,214) = 69336 / 2
LCM(324,214) = 34668
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FAQs on GCF of Fractions of 900/324, 5208/214
1. What is the HCF of 900,5208?
The HCF of 900,5208 is 12
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 900/324, 5208/214?
Answer: GCF of Numerators as per given numbers 900/324, 5208/214 is
GCF of Numerators i.e. for 900,5208 is 12
LCM of denominators i.e. for 324,214 is 34668.
Thus, GCF of Fractions is 12/34668.Finally, GCF of Fractions for 900/324, 5208/214 is 12/34668.