GCF of 1524/414, 9400/256
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1524/414, 9400/256 i.e 4/52992 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1524/414, 9400/256.
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 1524/414,9400/256?
Given fractions are 1524/414,9400/256
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 1524/414,9400/256, numerators are 1524,9400
Denominators are 414,256
The GCF of 1524,9400 is 4 .
LCM of 414,256 is 52992.
The greatest common factor of 1524/414,9400/256 = [GCF of 1524,9400]/[LCM of 414,256]= 4/52992
Therefore, the GCF of 1524/414,9400/256 is 4/52992.
To find the highest common factor of 1524,9400, we have to find the factors of both numbers and list the highest common factor.
The factors of 1524 are 1, 2, 3, 4, 6, 12, 127, 254, 381, 508, 762, 1524
The factors of 9400 are 1, 2, 4, 5, 8, 10, 20, 25, 40, 47, 50, 94, 100, 188, 200, 235, 376, 470, 940, 1175, 1880, 2350, 4700, 9400
The HCF of 1524,9400 is 4.
Lets's calculate GCF of 1524,9400
| 2 | 1524, 9400 |
| 2 | 762, 4700 |
| 381, 2350 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 1524,9400 By Matching Biggest Common Factor Method
Now, list down the factors of 1524
:1,2,3,4,6,12,127,254,381,508,762,1524
Now, list down the factors of 9400
:1,2,4,5,8,10,20,25,40,47,50,94,100,188,200,235,376,470,940,1175,1880,2350,4700,9400
Greatest Common Factor
We found the factors 1524,9400 . The biggest common factor number is the GCF number.
So the greatest common factor 1524,9400 is 4.
Lets's calculate LCM of 414,256
| 2 | 414, 256 |
| 207, 128 |
∴ So the LCM of the given numbers is 2 x 207 x 128 = 52992
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/52992
Therefore, the GCF of Fractions 1524/414,9400/256 is 4/52992
Least Common Multiple of 414,256 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 414,256 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,256) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(414,256) x common factors =2 x 1 = 2
LCM(414,256) = ( 414 × 256 ) / 2
LCM(414,256) = 105984 / 2
LCM(414,256) = 52992
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FAQs on GCF of Fractions of 1524/414, 9400/256
1. What is the HCF of 1524,9400?
The HCF of 1524,9400 is 4
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 1524/414, 9400/256?
Answer: GCF of Numerators as per given numbers 1524/414, 9400/256 is
GCF of Numerators i.e. for 1524,9400 is 4
LCM of denominators i.e. for 414,256 is 52992.
Thus, GCF of Fractions is 4/52992.Finally, GCF of Fractions for 1524/414, 9400/256 is 4/52992.