GCF of 8517/534, 1105/978
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 8517/534, 1105/978 i.e 17/87042 easily. The following is the detailed procedure to determine the greatest common factor of fractions 8517/534, 1105/978.
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 8517/534,1105/978?
Given fractions are 8517/534,1105/978
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 8517/534,1105/978, numerators are 8517,1105
Denominators are 534,978
The GCF of 8517,1105 is 17 .
LCM of 534,978 is 87042.
The greatest common factor of 8517/534,1105/978 = [GCF of 8517,1105]/[LCM of 534,978]= 17/87042
Therefore, the GCF of 8517/534,1105/978 is 17/87042.
To find the highest common factor of 8517,1105, we have to find the factors of both numbers and list the highest common factor.
The factors of 8517 are 1, 3, 17, 51, 167, 501, 2839, 8517
The factors of 1105 are 1, 5, 13, 17, 65, 85, 221, 1105
The HCF of 8517,1105 is 17.
Lets's calculate GCF of 8517,1105
| 17 | 8517, 1105 |
| 501, 65 |
∴ So the GCF of the given numbers is 17 = 17
Greatest Common Factor of 8517,1105 By Matching Biggest Common Factor Method
Now, list down the factors of 8517
:1,3,17,51,167,501,2839,8517
Now, list down the factors of 1105
:1,5,13,17,65,85,221,1105
Greatest Common Factor
We found the factors 8517,1105 . The biggest common factor number is the GCF number.
So the greatest common factor 8517,1105 is 17.
Lets's calculate LCM of 534,978
| 2 | 534, 978 |
| 3 | 267, 489 |
| 89, 163 |
∴ So the LCM of the given numbers is 2 x 3 x 89 x 163 = 87042
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/87042
Therefore, the GCF of Fractions 8517/534,1105/978 is 17/87042
Least Common Multiple of 534,978 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 534,978 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(534,978) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(534,978) x common factors =6 x 1 = 6
LCM(534,978) = ( 534 × 978 ) / 6
LCM(534,978) = 522252 / 6
LCM(534,978) = 87042
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FAQs on GCF of Fractions of 8517/534, 1105/978
1. What is the HCF of 8517,1105?
The HCF of 8517,1105 is 17
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 8517/534, 1105/978?
Answer: GCF of Numerators as per given numbers 8517/534, 1105/978 is
GCF of Numerators i.e. for 8517,1105 is 17
LCM of denominators i.e. for 534,978 is 87042.
Thus, GCF of Fractions is 17/87042.Finally, GCF of Fractions for 8517/534, 1105/978 is 17/87042.