GCF of 416/300, 2122/688
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 416/300, 2122/688 i.e 2/51600 easily. The following is the detailed procedure to determine the greatest common factor of fractions 416/300, 2122/688.
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 416/300,2122/688?
Given fractions are 416/300,2122/688
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 416/300,2122/688, numerators are 416,2122
Denominators are 300,688
The GCF of 416,2122 is 2 .
LCM of 300,688 is 51600.
The greatest common factor of 416/300,2122/688 = [GCF of 416,2122]/[LCM of 300,688]= 2/51600
Therefore, the GCF of 416/300,2122/688 is 2/51600.
To find the highest common factor of 416,2122, we have to find the factors of both numbers and list the highest common factor.
The factors of 416 are 1, 2, 4, 8, 13, 16, 26, 32, 52, 104, 208, 416
The factors of 2122 are 1, 2, 1061, 2122
The HCF of 416,2122 is 2.
Lets's calculate GCF of 416,2122
| 2 | 416, 2122 |
| 208, 1061 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 416,2122 By Matching Biggest Common Factor Method
Now, list down the factors of 416
:1,2,4,8,13,16,26,32,52,104,208,416
Now, list down the factors of 2122
:1,2,1061,2122
Greatest Common Factor
We found the factors 416,2122 . The biggest common factor number is the GCF number.
So the greatest common factor 416,2122 is 2.
Lets's calculate LCM of 300,688
| 2 | 300, 688 |
| 2 | 150, 344 |
| 75, 172 |
∴ So the LCM of the given numbers is 2 x 2 x 75 x 172 = 51600
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/51600
Therefore, the GCF of Fractions 416/300,2122/688 is 2/51600
Least Common Multiple of 300,688 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 300,688 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(300,688) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(300,688) x common factors =4 x 1 = 4
LCM(300,688) = ( 300 × 688 ) / 4
LCM(300,688) = 206400 / 4
LCM(300,688) = 51600
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FAQs on GCF of Fractions of 416/300, 2122/688
1. What is the HCF of 416,2122?
The HCF of 416,2122 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 416/300, 2122/688?
Answer: GCF of Numerators as per given numbers 416/300, 2122/688 is
GCF of Numerators i.e. for 416,2122 is 2
LCM of denominators i.e. for 300,688 is 51600.
Thus, GCF of Fractions is 2/51600.Finally, GCF of Fractions for 416/300, 2122/688 is 2/51600.