GCF of 102/307, 578/159, 216/521
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 102/307, 578/159, 216/521 i.e 2/25431573 easily. The following is the detailed procedure to determine the greatest common factor of fractions 102/307, 578/159, 216/521.
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 102/307,578/159,216/521?
Given fractions are 102/307,578/159,216/521
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 102/307,578/159,216/521, numerators are 102,578,216
Denominators are 307,159,521
The GCF of 102,578,216 is 2 .
LCM of 307,159,521 is 25431573.
The greatest common factor of 102/307,578/159,216/521 = [GCF of 102,578,216]/[LCM of 307,159,521]= 2/25431573
Therefore, the GCF of 102/307,578/159,216/521 is 2/25431573.
To find the highest common factor of 102,578,216, 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 578 are 1, 2, 17, 34, 289, 578
The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, 216
The HCF of 102,578,216 is 2.
Lets's calculate GCF of 102,578,216
| 2 | 102, 578, 216 |
| 51, 289, 108 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 102,578,216 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 578
:1,2,17,34,289,578
Now, list down the factors of 216
:1,2,3,4,6,8,9,12,18,24,27,36,54,72,108,216
Greatest Common Factor
We found the factors 102,578,216 . The biggest common factor number is the GCF number.
So the greatest common factor 102,578,216 is 2.
Lets's calculate LCM of 307,159,521
Given numbers has no common factors except 1. So, there LCM is their product i.e 25431573
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/25431573
Therefore, the GCF of Fractions 102/307,578/159,216/521 is 2/25431573
Least Common Multiple of 307,159,521 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 307,159,521 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(307,159,521) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(307,159,521) x common factors =1 x 1 = 1
LCM(307,159,521) = ( 307 × 159 × 521 ) / 1
LCM(307,159,521) = 25431573 / 1
LCM(307,159,521) = 25431573
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FAQs on GCF of Fractions of 102/307, 578/159, 216/521
1. What is the HCF of 102,578,216?
The HCF of 102,578,216 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 102/307, 578/159, 216/521?
Answer: GCF of Numerators as per given numbers 102/307, 578/159, 216/521 is
GCF of Numerators i.e. for 102,578,216 is 2
LCM of denominators i.e. for 307,159,521 is 25431573.
Thus, GCF of Fractions is 2/25431573.Finally, GCF of Fractions for 102/307, 578/159, 216/521 is 2/25431573.