GCF of 1824/409, 8322/150
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1824/409, 8322/150 i.e 114/61350 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1824/409, 8322/150.
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 1824/409,8322/150?
Given fractions are 1824/409,8322/150
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 1824/409,8322/150, numerators are 1824,8322
Denominators are 409,150
The GCF of 1824,8322 is 114 .
LCM of 409,150 is 61350.
The greatest common factor of 1824/409,8322/150 = [GCF of 1824,8322]/[LCM of 409,150]= 114/61350
Therefore, the GCF of 1824/409,8322/150 is 114/61350.
To find the highest common factor of 1824,8322, we have to find the factors of both numbers and list the highest common factor.
The factors of 1824 are 1, 2, 3, 4, 6, 8, 12, 16, 19, 24, 32, 38, 48, 57, 76, 96, 114, 152, 228, 304, 456, 608, 912, 1824
The factors of 8322 are 1, 2, 3, 6, 19, 38, 57, 73, 114, 146, 219, 438, 1387, 2774, 4161, 8322
The HCF of 1824,8322 is 114.
Lets's calculate GCF of 1824,8322
| 2 | 1824, 8322 |
| 3 | 912, 4161 |
| 19 | 304, 1387 |
| 16, 73 |
∴ So the GCF of the given numbers is 2 x 3 x 19 = 114
Greatest Common Factor of 1824,8322 By Matching Biggest Common Factor Method
Now, list down the factors of 1824
:1,2,3,4,6,8,12,16,19,24,32,38,48,57,76,96,114,152,228,304,456,608,912,1824
Now, list down the factors of 8322
:1,2,3,6,19,38,57,73,114,146,219,438,1387,2774,4161,8322
Greatest Common Factor
We found the factors 1824,8322 . The biggest common factor number is the GCF number.
So the greatest common factor 1824,8322 is 114.
Lets's calculate LCM of 409,150
Given numbers has no common factors except 1. So, there LCM is their product i.e 61350
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 114/61350
Therefore, the GCF of Fractions 1824/409,8322/150 is 114/61350
Least Common Multiple of 409,150 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 409,150 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(409,150) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(409,150) x common factors =1 x 1 = 1
LCM(409,150) = ( 409 × 150 ) / 1
LCM(409,150) = 61350 / 1
LCM(409,150) = 61350
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FAQs on GCF of Fractions of 1824/409, 8322/150
1. What is the HCF of 1824,8322?
The HCF of 1824,8322 is 114
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 1824/409, 8322/150?
Answer: GCF of Numerators as per given numbers 1824/409, 8322/150 is
GCF of Numerators i.e. for 1824,8322 is 114
LCM of denominators i.e. for 409,150 is 61350.
Thus, GCF of Fractions is 114/61350.Finally, GCF of Fractions for 1824/409, 8322/150 is 114/61350.