GCF of 102/171, 289/674
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 102/171, 289/674 i.e 17/115254 easily. The following is the detailed procedure to determine the greatest common factor of fractions 102/171, 289/674.
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 102/171,289/674?
Given fractions are 102/171,289/674
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 102/171,289/674, numerators are 102,289
Denominators are 171,674
The GCF of 102,289 is 17 .
LCM of 171,674 is 115254.
The greatest common factor of 102/171,289/674 = [GCF of 102,289]/[LCM of 171,674]= 17/115254
Therefore, the GCF of 102/171,289/674 is 17/115254.
To find the highest common factor of 102,289, we have to find the factors of both numbers and list the highest common factor.
The factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102
The factors of 289 are 1, 17, 289
The HCF of 102,289 is 17.
Lets's calculate GCF of 102,289
| 17 | 102, 289 |
| 6, 17 |
∴ So the GCF of the given numbers is 17 = 17
Greatest Common Factor of 102,289 By Matching Biggest Common Factor Method
Now, list down the factors of 102
:1,2,3,6,17,34,51,102
Now, list down the factors of 289
:1,17,289
Greatest Common Factor
We found the factors 102,289 . The biggest common factor number is the GCF number.
So the greatest common factor 102,289 is 17.
Lets's calculate LCM of 171,674
Given numbers has no common factors except 1. So, there LCM is their product i.e 115254
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/115254
Therefore, the GCF of Fractions 102/171,289/674 is 17/115254
Least Common Multiple of 171,674 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 171,674 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(171,674) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(171,674) x common factors =1 x 1 = 1
LCM(171,674) = ( 171 × 674 ) / 1
LCM(171,674) = 115254 / 1
LCM(171,674) = 115254
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FAQs on GCF of Fractions of 102/171, 289/674
1. What is the HCF of 102,289?
The HCF of 102,289 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 102/171, 289/674?
Answer: GCF of Numerators as per given numbers 102/171, 289/674 is
GCF of Numerators i.e. for 102,289 is 17
LCM of denominators i.e. for 171,674 is 115254.
Thus, GCF of Fractions is 17/115254.Finally, GCF of Fractions for 102/171, 289/674 is 17/115254.