GCF of 4000/742, 6100/977
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 4000/742, 6100/977 i.e 100/724934 easily. The following is the detailed procedure to determine the greatest common factor of fractions 4000/742, 6100/977.
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 4000/742,6100/977?
Given fractions are 4000/742,6100/977
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 4000/742,6100/977, numerators are 4000,6100
Denominators are 742,977
The GCF of 4000,6100 is 100 .
LCM of 742,977 is 724934.
The greatest common factor of 4000/742,6100/977 = [GCF of 4000,6100]/[LCM of 742,977]= 100/724934
Therefore, the GCF of 4000/742,6100/977 is 100/724934.
To find the highest common factor of 4000,6100, we have to find the factors of both numbers and list the highest common factor.
The factors of 4000 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 80, 100, 125, 160, 200, 250, 400, 500, 800, 1000, 2000, 4000
The factors of 6100 are 1, 2, 4, 5, 10, 20, 25, 50, 61, 100, 122, 244, 305, 610, 1220, 1525, 3050, 6100
The HCF of 4000,6100 is 100.
Lets's calculate GCF of 4000,6100
| 2 | 4000, 6100 |
| 2 | 2000, 3050 |
| 5 | 1000, 1525 |
| 5 | 200, 305 |
| 40, 61 |
∴ So the GCF of the given numbers is 2 x 2 x 5 x 5 = 100
Greatest Common Factor of 4000,6100 By Matching Biggest Common Factor Method
Now, list down the factors of 4000
:1,2,4,5,8,10,16,20,25,32,40,50,80,100,125,160,200,250,400,500,800,1000,2000,4000
Now, list down the factors of 6100
:1,2,4,5,10,20,25,50,61,100,122,244,305,610,1220,1525,3050,6100
Greatest Common Factor
We found the factors 4000,6100 . The biggest common factor number is the GCF number.
So the greatest common factor 4000,6100 is 100.
Lets's calculate LCM of 742,977
Given numbers has no common factors except 1. So, there LCM is their product i.e 724934
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 100/724934
Therefore, the GCF of Fractions 4000/742,6100/977 is 100/724934
Least Common Multiple of 742,977 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 742,977 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(742,977) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(742,977) x common factors =1 x 1 = 1
LCM(742,977) = ( 742 × 977 ) / 1
LCM(742,977) = 724934 / 1
LCM(742,977) = 724934
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FAQs on GCF of Fractions of 4000/742, 6100/977
1. What is the HCF of 4000,6100?
The HCF of 4000,6100 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 4000/742, 6100/977?
Answer: GCF of Numerators as per given numbers 4000/742, 6100/977 is
GCF of Numerators i.e. for 4000,6100 is 100
LCM of denominators i.e. for 742,977 is 724934.
Thus, GCF of Fractions is 100/724934.Finally, GCF of Fractions for 4000/742, 6100/977 is 100/724934.