GCF of 746/60, 678/586
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 746/60, 678/586 i.e 2/17580 easily. The following is the detailed procedure to determine the greatest common factor of fractions 746/60, 678/586.
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 746/60,678/586?
Given fractions are 746/60,678/586
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 746/60,678/586, numerators are 746,678
Denominators are 60,586
The GCF of 746,678 is 2 .
LCM of 60,586 is 17580.
The greatest common factor of 746/60,678/586 = [GCF of 746,678]/[LCM of 60,586]= 2/17580
Therefore, the GCF of 746/60,678/586 is 2/17580.
To find the highest common factor of 746,678, we have to find the factors of both numbers and list the highest common factor.
The factors of 746 are 1, 2, 373, 746
The factors of 678 are 1, 2, 3, 6, 113, 226, 339, 678
The HCF of 746,678 is 2.
Lets's calculate GCF of 746,678
| 2 | 746, 678 |
| 373, 339 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 746,678 By Matching Biggest Common Factor Method
Now, list down the factors of 746
:1,2,373,746
Now, list down the factors of 678
:1,2,3,6,113,226,339,678
Greatest Common Factor
We found the factors 746,678 . The biggest common factor number is the GCF number.
So the greatest common factor 746,678 is 2.
Lets's calculate LCM of 60,586
| 2 | 60, 586 |
| 30, 293 |
∴ So the LCM of the given numbers is 2 x 30 x 293 = 17580
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/17580
Therefore, the GCF of Fractions 746/60,678/586 is 2/17580
Least Common Multiple of 60,586 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 60,586 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(60,586) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(60,586) x common factors =2 x 1 = 2
LCM(60,586) = ( 60 × 586 ) / 2
LCM(60,586) = 35160 / 2
LCM(60,586) = 17580
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FAQs on GCF of Fractions of 746/60, 678/586
1. What is the HCF of 746,678?
The HCF of 746,678 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 746/60, 678/586?
Answer: GCF of Numerators as per given numbers 746/60, 678/586 is
GCF of Numerators i.e. for 746,678 is 2
LCM of denominators i.e. for 60,586 is 17580.
Thus, GCF of Fractions is 2/17580.Finally, GCF of Fractions for 746/60, 678/586 is 2/17580.