GCF of 658/589, 728/670
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 658/589, 728/670 i.e 14/394630 easily. The following is the detailed procedure to determine the greatest common factor of fractions 658/589, 728/670.
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 658/589,728/670?
Given fractions are 658/589,728/670
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 658/589,728/670, numerators are 658,728
Denominators are 589,670
The GCF of 658,728 is 14 .
LCM of 589,670 is 394630.
The greatest common factor of 658/589,728/670 = [GCF of 658,728]/[LCM of 589,670]= 14/394630
Therefore, the GCF of 658/589,728/670 is 14/394630.
To find the highest common factor of 658,728, we have to find the factors of both numbers and list the highest common factor.
The factors of 658 are 1, 2, 7, 14, 47, 94, 329, 658
The factors of 728 are 1, 2, 4, 7, 8, 13, 14, 26, 28, 52, 56, 91, 104, 182, 364, 728
The HCF of 658,728 is 14.
Lets's calculate GCF of 658,728
| 2 | 658, 728 |
| 7 | 329, 364 |
| 47, 52 |
∴ So the GCF of the given numbers is 2 x 7 = 14
Greatest Common Factor of 658,728 By Matching Biggest Common Factor Method
Now, list down the factors of 658
:1,2,7,14,47,94,329,658
Now, list down the factors of 728
:1,2,4,7,8,13,14,26,28,52,56,91,104,182,364,728
Greatest Common Factor
We found the factors 658,728 . The biggest common factor number is the GCF number.
So the greatest common factor 658,728 is 14.
Lets's calculate LCM of 589,670
Given numbers has no common factors except 1. So, there LCM is their product i.e 394630
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 14/394630
Therefore, the GCF of Fractions 658/589,728/670 is 14/394630
Least Common Multiple of 589,670 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 589,670 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(589,670) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(589,670) x common factors =1 x 1 = 1
LCM(589,670) = ( 589 × 670 ) / 1
LCM(589,670) = 394630 / 1
LCM(589,670) = 394630
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FAQs on GCF of Fractions of 658/589, 728/670
1. What is the HCF of 658,728?
The HCF of 658,728 is 14
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 658/589, 728/670?
Answer: GCF of Numerators as per given numbers 658/589, 728/670 is
GCF of Numerators i.e. for 658,728 is 14
LCM of denominators i.e. for 589,670 is 394630.
Thus, GCF of Fractions is 14/394630.Finally, GCF of Fractions for 658/589, 728/670 is 14/394630.