GCF of 6984/430, 7824/218
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6984/430, 7824/218 i.e 24/46870 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6984/430, 7824/218.
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 6984/430,7824/218?
Given fractions are 6984/430,7824/218
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 6984/430,7824/218, numerators are 6984,7824
Denominators are 430,218
The GCF of 6984,7824 is 24 .
LCM of 430,218 is 46870.
The greatest common factor of 6984/430,7824/218 = [GCF of 6984,7824]/[LCM of 430,218]= 24/46870
Therefore, the GCF of 6984/430,7824/218 is 24/46870.
To find the highest common factor of 6984,7824, we have to find the factors of both numbers and list the highest common factor.
The factors of 6984 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 97, 194, 291, 388, 582, 776, 873, 1164, 1746, 2328, 3492, 6984
The factors of 7824 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48, 163, 326, 489, 652, 978, 1304, 1956, 2608, 3912, 7824
The HCF of 6984,7824 is 24.
Lets's calculate GCF of 6984,7824
| 2 | 6984, 7824 |
| 2 | 3492, 3912 |
| 2 | 1746, 1956 |
| 3 | 873, 978 |
| 291, 326 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 3 = 24
Greatest Common Factor of 6984,7824 By Matching Biggest Common Factor Method
Now, list down the factors of 6984
:1,2,3,4,6,8,9,12,18,24,36,72,97,194,291,388,582,776,873,1164,1746,2328,3492,6984
Now, list down the factors of 7824
:1,2,3,4,6,8,12,16,24,48,163,326,489,652,978,1304,1956,2608,3912,7824
Greatest Common Factor
We found the factors 6984,7824 . The biggest common factor number is the GCF number.
So the greatest common factor 6984,7824 is 24.
Lets's calculate LCM of 430,218
| 2 | 430, 218 |
| 215, 109 |
∴ So the LCM of the given numbers is 2 x 215 x 109 = 46870
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 24/46870
Therefore, the GCF of Fractions 6984/430,7824/218 is 24/46870
Least Common Multiple of 430,218 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 430,218 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(430,218) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(430,218) x common factors =2 x 1 = 2
LCM(430,218) = ( 430 × 218 ) / 2
LCM(430,218) = 93740 / 2
LCM(430,218) = 46870
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FAQs on GCF of Fractions of 6984/430, 7824/218
1. What is the HCF of 6984,7824?
The HCF of 6984,7824 is 24
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 6984/430, 7824/218?
Answer: GCF of Numerators as per given numbers 6984/430, 7824/218 is
GCF of Numerators i.e. for 6984,7824 is 24
LCM of denominators i.e. for 430,218 is 46870.
Thus, GCF of Fractions is 24/46870.Finally, GCF of Fractions for 6984/430, 7824/218 is 24/46870.