GCF of 400/204, 6500/661
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 400/204, 6500/661 i.e 100/134844 easily. The following is the detailed procedure to determine the greatest common factor of fractions 400/204, 6500/661.
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 400/204,6500/661?
Given fractions are 400/204,6500/661
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 400/204,6500/661, numerators are 400,6500
Denominators are 204,661
The GCF of 400,6500 is 100 .
LCM of 204,661 is 134844.
The greatest common factor of 400/204,6500/661 = [GCF of 400,6500]/[LCM of 204,661]= 100/134844
Therefore, the GCF of 400/204,6500/661 is 100/134844.
To find the highest common factor of 400,6500, we have to find the factors of both numbers and list the highest common factor.
The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
The factors of 6500 are 1, 2, 4, 5, 10, 13, 20, 25, 26, 50, 52, 65, 100, 125, 130, 250, 260, 325, 500, 650, 1300, 1625, 3250, 6500
The HCF of 400,6500 is 100.
Lets's calculate GCF of 400,6500
| 2 | 400, 6500 |
| 2 | 200, 3250 |
| 5 | 100, 1625 |
| 5 | 20, 325 |
| 4, 65 |
∴ So the GCF of the given numbers is 2 x 2 x 5 x 5 = 100
Greatest Common Factor of 400,6500 By Matching Biggest Common Factor Method
Now, list down the factors of 400
:1,2,4,5,8,10,16,20,25,40,50,80,100,200,400
Now, list down the factors of 6500
:1,2,4,5,10,13,20,25,26,50,52,65,100,125,130,250,260,325,500,650,1300,1625,3250,6500
Greatest Common Factor
We found the factors 400,6500 . The biggest common factor number is the GCF number.
So the greatest common factor 400,6500 is 100.
Lets's calculate LCM of 204,661
Given numbers has no common factors except 1. So, there LCM is their product i.e 134844
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 100/134844
Therefore, the GCF of Fractions 400/204,6500/661 is 100/134844
Least Common Multiple of 204,661 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 204,661 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(204,661) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(204,661) x common factors =1 x 1 = 1
LCM(204,661) = ( 204 × 661 ) / 1
LCM(204,661) = 134844 / 1
LCM(204,661) = 134844
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FAQs on GCF of Fractions of 400/204, 6500/661
1. What is the HCF of 400,6500?
The HCF of 400,6500 is 100
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 400/204, 6500/661?
Answer: GCF of Numerators as per given numbers 400/204, 6500/661 is
GCF of Numerators i.e. for 400,6500 is 100
LCM of denominators i.e. for 204,661 is 134844.
Thus, GCF of Fractions is 100/134844.Finally, GCF of Fractions for 400/204, 6500/661 is 100/134844.