GCF of 457/14, 670/80, 978/96
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 457/14, 670/80, 978/96 i.e 1/3360 easily. The following is the detailed procedure to determine the greatest common factor of fractions 457/14, 670/80, 978/96.
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 457/14,670/80,978/96?
Given fractions are 457/14,670/80,978/96
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 457/14,670/80,978/96, numerators are 457,670,978
Denominators are 14,80,96
The GCF of 457,670,978 is 1 .
LCM of 14,80,96 is 3360.
The greatest common factor of 457/14,670/80,978/96 = [GCF of 457,670,978]/[LCM of 14,80,96]= 1/3360
Therefore, the GCF of 457/14,670/80,978/96 is 1/3360.
To find the highest common factor of 457,670,978, we have to find the factors of both numbers and list the highest common factor.
The factors of 457 are 1, 457
The factors of 670 are 1, 2, 5, 10, 67, 134, 335, 670
The factors of 978 are 1, 2, 3, 6, 163, 326, 489, 978
The HCF of 457,670,978 is 1.
Lets's calculate GCF of 457,670,978
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 457,670,978 By Matching Biggest Common Factor Method
Now, list down the factors of 457
:1,457
Now, list down the factors of 670
:1,2,5,10,67,134,335,670
Now, list down the factors of 978
:1,2,3,6,163,326,489,978
Greatest Common Factor
We found the factors 457,670,978 . The biggest common factor number is the GCF number.
So the greatest common factor 457,670,978 is 1.
Lets's calculate LCM of 14,80,96
| 2 | 14, 80, 96 |
| 2 | 7, 40, 48 |
| 2 | 7, 20, 24 |
| 2 | 7, 10, 12 |
| 7, 5, 6 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 7 x 5 x 6 = 3360
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3360
Therefore, the GCF of Fractions 457/14,670/80,978/96 is 1/3360
Least Common Multiple of 14,80,96 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 14,80,96 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,80,96) = 2
common factors(in case of two or more numbers have common factors) = 16
GCF(14,80,96) x common factors =2 x 16 = 32
LCM(14,80,96) = ( 14 × 80 × 96 ) / 32
LCM(14,80,96) = 107520 / 32
LCM(14,80,96) = 3360
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FAQs on GCF of Fractions of 457/14, 670/80, 978/96
1. What is the HCF of 457,670,978?
The HCF of 457,670,978 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 457/14, 670/80, 978/96?
Answer: GCF of Numerators as per given numbers 457/14, 670/80, 978/96 is
GCF of Numerators i.e. for 457,670,978 is 1
LCM of denominators i.e. for 14,80,96 is 3360.
Thus, GCF of Fractions is 1/3360.Finally, GCF of Fractions for 457/14, 670/80, 978/96 is 1/3360.