GCF of 665/15, 978/414
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 665/15, 978/414 i.e 1/2070 easily. The following is the detailed procedure to determine the greatest common factor of fractions 665/15, 978/414.
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 665/15,978/414?
Given fractions are 665/15,978/414
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 665/15,978/414, numerators are 665,978
Denominators are 15,414
The GCF of 665,978 is 1 .
LCM of 15,414 is 2070.
The greatest common factor of 665/15,978/414 = [GCF of 665,978]/[LCM of 15,414]= 1/2070
Therefore, the GCF of 665/15,978/414 is 1/2070.
To find the highest common factor of 665,978, we have to find the factors of both numbers and list the highest common factor.
The factors of 665 are 1, 5, 7, 19, 35, 95, 133, 665
The factors of 978 are 1, 2, 3, 6, 163, 326, 489, 978
The HCF of 665,978 is 1.
Lets's calculate GCF of 665,978
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 665,978 By Matching Biggest Common Factor Method
Now, list down the factors of 665
:1,5,7,19,35,95,133,665
Now, list down the factors of 978
:1,2,3,6,163,326,489,978
Greatest Common Factor
We found the factors 665,978 . The biggest common factor number is the GCF number.
So the greatest common factor 665,978 is 1.
Lets's calculate LCM of 15,414
| 3 | 15, 414 |
| 5, 138 |
∴ So the LCM of the given numbers is 3 x 5 x 138 = 2070
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2070
Therefore, the GCF of Fractions 665/15,978/414 is 1/2070
Least Common Multiple of 15,414 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 15,414 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(15,414) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(15,414) x common factors =3 x 1 = 3
LCM(15,414) = ( 15 × 414 ) / 3
LCM(15,414) = 6210 / 3
LCM(15,414) = 2070
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FAQs on GCF of Fractions of 665/15, 978/414
1. What is the HCF of 665,978?
The HCF of 665,978 is 1
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 665/15, 978/414?
Answer: GCF of Numerators as per given numbers 665/15, 978/414 is
GCF of Numerators i.e. for 665,978 is 1
LCM of denominators i.e. for 15,414 is 2070.
Thus, GCF of Fractions is 1/2070.Finally, GCF of Fractions for 665/15, 978/414 is 1/2070.