GCF of 854/840, 1984/368
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 854/840, 1984/368 i.e 2/38640 easily. The following is the detailed procedure to determine the greatest common factor of fractions 854/840, 1984/368.
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 854/840,1984/368?
Given fractions are 854/840,1984/368
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 854/840,1984/368, numerators are 854,1984
Denominators are 840,368
The GCF of 854,1984 is 2 .
LCM of 840,368 is 38640.
The greatest common factor of 854/840,1984/368 = [GCF of 854,1984]/[LCM of 840,368]= 2/38640
Therefore, the GCF of 854/840,1984/368 is 2/38640.
To find the highest common factor of 854,1984, we have to find the factors of both numbers and list the highest common factor.
The factors of 854 are 1, 2, 7, 14, 61, 122, 427, 854
The factors of 1984 are 1, 2, 4, 8, 16, 31, 32, 62, 64, 124, 248, 496, 992, 1984
The HCF of 854,1984 is 2.
Lets's calculate GCF of 854,1984
| 2 | 854, 1984 |
| 427, 992 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 854,1984 By Matching Biggest Common Factor Method
Now, list down the factors of 854
:1,2,7,14,61,122,427,854
Now, list down the factors of 1984
:1,2,4,8,16,31,32,62,64,124,248,496,992,1984
Greatest Common Factor
We found the factors 854,1984 . The biggest common factor number is the GCF number.
So the greatest common factor 854,1984 is 2.
Lets's calculate LCM of 840,368
| 2 | 840, 368 |
| 2 | 420, 184 |
| 2 | 210, 92 |
| 105, 46 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 105 x 46 = 38640
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/38640
Therefore, the GCF of Fractions 854/840,1984/368 is 2/38640
Least Common Multiple of 840,368 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 840,368 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(840,368) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(840,368) x common factors =8 x 1 = 8
LCM(840,368) = ( 840 × 368 ) / 8
LCM(840,368) = 309120 / 8
LCM(840,368) = 38640
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FAQs on GCF of Fractions of 854/840, 1984/368
1. What is the HCF of 854,1984?
The HCF of 854,1984 is 2
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 854/840, 1984/368?
Answer: GCF of Numerators as per given numbers 854/840, 1984/368 is
GCF of Numerators i.e. for 854,1984 is 2
LCM of denominators i.e. for 840,368 is 38640.
Thus, GCF of Fractions is 2/38640.Finally, GCF of Fractions for 854/840, 1984/368 is 2/38640.