GCF of 5117/104, 9968/7284
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5117/104, 9968/7284 i.e 7/189384 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5117/104, 9968/7284.
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 5117/104,9968/7284?
Given fractions are 5117/104,9968/7284
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 5117/104,9968/7284, numerators are 5117,9968
Denominators are 104,7284
The GCF of 5117,9968 is 7 .
LCM of 104,7284 is 189384.
The greatest common factor of 5117/104,9968/7284 = [GCF of 5117,9968]/[LCM of 104,7284]= 7/189384
Therefore, the GCF of 5117/104,9968/7284 is 7/189384.
To find the highest common factor of 5117,9968, we have to find the factors of both numbers and list the highest common factor.
The factors of 5117 are 1, 7, 17, 43, 119, 301, 731, 5117
The factors of 9968 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 89, 112, 178, 356, 623, 712, 1246, 1424, 2492, 4984, 9968
The HCF of 5117,9968 is 7.
Lets's calculate GCF of 5117,9968
| 7 | 5117, 9968 |
| 731, 1424 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 5117,9968 By Matching Biggest Common Factor Method
Now, list down the factors of 5117
:1,7,17,43,119,301,731,5117
Now, list down the factors of 9968
:1,2,4,7,8,14,16,28,56,89,112,178,356,623,712,1246,1424,2492,4984,9968
Greatest Common Factor
We found the factors 5117,9968 . The biggest common factor number is the GCF number.
So the greatest common factor 5117,9968 is 7.
Lets's calculate LCM of 104,7284
| 2 | 104, 7284 |
| 2 | 52, 3642 |
| 26, 1821 |
∴ So the LCM of the given numbers is 2 x 2 x 26 x 1821 = 189384
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/189384
Therefore, the GCF of Fractions 5117/104,9968/7284 is 7/189384
Least Common Multiple of 104,7284 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 104,7284 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(104,7284) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(104,7284) x common factors =4 x 1 = 4
LCM(104,7284) = ( 104 × 7284 ) / 4
LCM(104,7284) = 757536 / 4
LCM(104,7284) = 189384
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FAQs on GCF of Fractions of 5117/104, 9968/7284
1. What is the HCF of 5117,9968?
The HCF of 5117,9968 is 7
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 5117/104, 9968/7284?
Answer: GCF of Numerators as per given numbers 5117/104, 9968/7284 is
GCF of Numerators i.e. for 5117,9968 is 7
LCM of denominators i.e. for 104,7284 is 189384.
Thus, GCF of Fractions is 7/189384.Finally, GCF of Fractions for 5117/104, 9968/7284 is 7/189384.