GCF of 170/309, 7854/660
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 170/309, 7854/660 i.e 34/67980 easily. The following is the detailed procedure to determine the greatest common factor of fractions 170/309, 7854/660.
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 170/309,7854/660?
Given fractions are 170/309,7854/660
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 170/309,7854/660, numerators are 170,7854
Denominators are 309,660
The GCF of 170,7854 is 34 .
LCM of 309,660 is 67980.
The greatest common factor of 170/309,7854/660 = [GCF of 170,7854]/[LCM of 309,660]= 34/67980
Therefore, the GCF of 170/309,7854/660 is 34/67980.
To find the highest common factor of 170,7854, we have to find the factors of both numbers and list the highest common factor.
The factors of 170 are 1, 2, 5, 10, 17, 34, 85, 170
The factors of 7854 are 1, 2, 3, 6, 7, 11, 14, 17, 21, 22, 33, 34, 42, 51, 66, 77, 102, 119, 154, 187, 231, 238, 357, 374, 462, 561, 714, 1122, 1309, 2618, 3927, 7854
The HCF of 170,7854 is 34.
Lets's calculate GCF of 170,7854
| 2 | 170, 7854 |
| 17 | 85, 3927 |
| 5, 231 |
∴ So the GCF of the given numbers is 2 x 17 = 34
Greatest Common Factor of 170,7854 By Matching Biggest Common Factor Method
Now, list down the factors of 170
:1,2,5,10,17,34,85,170
Now, list down the factors of 7854
:1,2,3,6,7,11,14,17,21,22,33,34,42,51,66,77,102,119,154,187,231,238,357,374,462,561,714,1122,1309,2618,3927,7854
Greatest Common Factor
We found the factors 170,7854 . The biggest common factor number is the GCF number.
So the greatest common factor 170,7854 is 34.
Lets's calculate LCM of 309,660
| 3 | 309, 660 |
| 103, 220 |
∴ So the LCM of the given numbers is 3 x 103 x 220 = 67980
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 34/67980
Therefore, the GCF of Fractions 170/309,7854/660 is 34/67980
Least Common Multiple of 309,660 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 309,660 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(309,660) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(309,660) x common factors =3 x 1 = 3
LCM(309,660) = ( 309 × 660 ) / 3
LCM(309,660) = 203940 / 3
LCM(309,660) = 67980
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FAQs on GCF of Fractions of 170/309, 7854/660
1. What is the HCF of 170,7854?
The HCF of 170,7854 is 34
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 170/309, 7854/660?
Answer: GCF of Numerators as per given numbers 170/309, 7854/660 is
GCF of Numerators i.e. for 170,7854 is 34
LCM of denominators i.e. for 309,660 is 67980.
Thus, GCF of Fractions is 34/67980.Finally, GCF of Fractions for 170/309, 7854/660 is 34/67980.