GCF of 2678/158, 1200/3668
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2678/158, 1200/3668 i.e 2/289772 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2678/158, 1200/3668.
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 2678/158,1200/3668?
Given fractions are 2678/158,1200/3668
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 2678/158,1200/3668, numerators are 2678,1200
Denominators are 158,3668
The GCF of 2678,1200 is 2 .
LCM of 158,3668 is 289772.
The greatest common factor of 2678/158,1200/3668 = [GCF of 2678,1200]/[LCM of 158,3668]= 2/289772
Therefore, the GCF of 2678/158,1200/3668 is 2/289772.
To find the highest common factor of 2678,1200, we have to find the factors of both numbers and list the highest common factor.
The factors of 2678 are 1, 2, 13, 26, 103, 206, 1339, 2678
The factors of 1200 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200
The HCF of 2678,1200 is 2.
Lets's calculate GCF of 2678,1200
| 2 | 2678, 1200 |
| 1339, 600 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 2678,1200 By Matching Biggest Common Factor Method
Now, list down the factors of 2678
:1,2,13,26,103,206,1339,2678
Now, list down the factors of 1200
:1,2,3,4,5,6,8,10,12,15,16,20,24,25,30,40,48,50,60,75,80,100,120,150,200,240,300,400,600,1200
Greatest Common Factor
We found the factors 2678,1200 . The biggest common factor number is the GCF number.
So the greatest common factor 2678,1200 is 2.
Lets's calculate LCM of 158,3668
| 2 | 158, 3668 |
| 79, 1834 |
∴ So the LCM of the given numbers is 2 x 79 x 1834 = 289772
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/289772
Therefore, the GCF of Fractions 2678/158,1200/3668 is 2/289772
Least Common Multiple of 158,3668 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 158,3668 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(158,3668) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(158,3668) x common factors =2 x 1 = 2
LCM(158,3668) = ( 158 × 3668 ) / 2
LCM(158,3668) = 579544 / 2
LCM(158,3668) = 289772
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FAQs on GCF of Fractions of 2678/158, 1200/3668
1. What is the HCF of 2678,1200?
The HCF of 2678,1200 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 2678/158, 1200/3668?
Answer: GCF of Numerators as per given numbers 2678/158, 1200/3668 is
GCF of Numerators i.e. for 2678,1200 is 2
LCM of denominators i.e. for 158,3668 is 289772.
Thus, GCF of Fractions is 2/289772.Finally, GCF of Fractions for 2678/158, 1200/3668 is 2/289772.