GCF of 7400/654, 8350/5614
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7400/654, 8350/5614 i.e 50/1835778 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7400/654, 8350/5614.
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 7400/654,8350/5614?
Given fractions are 7400/654,8350/5614
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 7400/654,8350/5614, numerators are 7400,8350
Denominators are 654,5614
The GCF of 7400,8350 is 50 .
LCM of 654,5614 is 1835778.
The greatest common factor of 7400/654,8350/5614 = [GCF of 7400,8350]/[LCM of 654,5614]= 50/1835778
Therefore, the GCF of 7400/654,8350/5614 is 50/1835778.
To find the highest common factor of 7400,8350, we have to find the factors of both numbers and list the highest common factor.
The factors of 7400 are 1, 2, 4, 5, 8, 10, 20, 25, 37, 40, 50, 74, 100, 148, 185, 200, 296, 370, 740, 925, 1480, 1850, 3700, 7400
The factors of 8350 are 1, 2, 5, 10, 25, 50, 167, 334, 835, 1670, 4175, 8350
The HCF of 7400,8350 is 50.
Lets's calculate GCF of 7400,8350
| 2 | 7400, 8350 |
| 5 | 3700, 4175 |
| 5 | 740, 835 |
| 148, 167 |
∴ So the GCF of the given numbers is 2 x 5 x 5 = 50
Greatest Common Factor of 7400,8350 By Matching Biggest Common Factor Method
Now, list down the factors of 7400
:1,2,4,5,8,10,20,25,37,40,50,74,100,148,185,200,296,370,740,925,1480,1850,3700,7400
Now, list down the factors of 8350
:1,2,5,10,25,50,167,334,835,1670,4175,8350
Greatest Common Factor
We found the factors 7400,8350 . The biggest common factor number is the GCF number.
So the greatest common factor 7400,8350 is 50.
Lets's calculate LCM of 654,5614
| 2 | 654, 5614 |
| 327, 2807 |
∴ So the LCM of the given numbers is 2 x 327 x 2807 = 1835778
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 50/1835778
Therefore, the GCF of Fractions 7400/654,8350/5614 is 50/1835778
Least Common Multiple of 654,5614 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 654,5614 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(654,5614) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(654,5614) x common factors =2 x 1 = 2
LCM(654,5614) = ( 654 × 5614 ) / 2
LCM(654,5614) = 3671556 / 2
LCM(654,5614) = 1835778
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FAQs on GCF of Fractions of 7400/654, 8350/5614
1. What is the HCF of 7400,8350?
The HCF of 7400,8350 is 50
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 7400/654, 8350/5614?
Answer: GCF of Numerators as per given numbers 7400/654, 8350/5614 is
GCF of Numerators i.e. for 7400,8350 is 50
LCM of denominators i.e. for 654,5614 is 1835778.
Thus, GCF of Fractions is 50/1835778.Finally, GCF of Fractions for 7400/654, 8350/5614 is 50/1835778.