GCF of 7973/384, 5474/682
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7973/384, 5474/682 i.e 119/130944 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7973/384, 5474/682.
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 7973/384,5474/682?
Given fractions are 7973/384,5474/682
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 7973/384,5474/682, numerators are 7973,5474
Denominators are 384,682
The GCF of 7973,5474 is 119 .
LCM of 384,682 is 130944.
The greatest common factor of 7973/384,5474/682 = [GCF of 7973,5474]/[LCM of 384,682]= 119/130944
Therefore, the GCF of 7973/384,5474/682 is 119/130944.
To find the highest common factor of 7973,5474, we have to find the factors of both numbers and list the highest common factor.
The factors of 7973 are 1, 7, 17, 67, 119, 469, 1139, 7973
The factors of 5474 are 1, 2, 7, 14, 17, 23, 34, 46, 119, 161, 238, 322, 391, 782, 2737, 5474
The HCF of 7973,5474 is 119.
Lets's calculate GCF of 7973,5474
| 7 | 7973, 5474 |
| 17 | 1139, 782 |
| 67, 46 |
∴ So the GCF of the given numbers is 7 x 17 = 119
Greatest Common Factor of 7973,5474 By Matching Biggest Common Factor Method
Now, list down the factors of 7973
:1,7,17,67,119,469,1139,7973
Now, list down the factors of 5474
:1,2,7,14,17,23,34,46,119,161,238,322,391,782,2737,5474
Greatest Common Factor
We found the factors 7973,5474 . The biggest common factor number is the GCF number.
So the greatest common factor 7973,5474 is 119.
Lets's calculate LCM of 384,682
| 2 | 384, 682 |
| 192, 341 |
∴ So the LCM of the given numbers is 2 x 192 x 341 = 130944
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 119/130944
Therefore, the GCF of Fractions 7973/384,5474/682 is 119/130944
Least Common Multiple of 384,682 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 384,682 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(384,682) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(384,682) x common factors =2 x 1 = 2
LCM(384,682) = ( 384 × 682 ) / 2
LCM(384,682) = 261888 / 2
LCM(384,682) = 130944
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FAQs on GCF of Fractions of 7973/384, 5474/682
1. What is the HCF of 7973,5474?
The HCF of 7973,5474 is 119
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 7973/384, 5474/682?
Answer: GCF of Numerators as per given numbers 7973/384, 5474/682 is
GCF of Numerators i.e. for 7973,5474 is 119
LCM of denominators i.e. for 384,682 is 130944.
Thus, GCF of Fractions is 119/130944.Finally, GCF of Fractions for 7973/384, 5474/682 is 119/130944.