GCF of 1729/420, 6065/7500
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1729/420, 6065/7500 i.e 1/52500 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1729/420, 6065/7500.
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 1729/420,6065/7500?
Given fractions are 1729/420,6065/7500
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 1729/420,6065/7500, numerators are 1729,6065
Denominators are 420,7500
The GCF of 1729,6065 is 1 .
LCM of 420,7500 is 52500.
The greatest common factor of 1729/420,6065/7500 = [GCF of 1729,6065]/[LCM of 420,7500]= 1/52500
Therefore, the GCF of 1729/420,6065/7500 is 1/52500.
To find the highest common factor of 1729,6065, we have to find the factors of both numbers and list the highest common factor.
The factors of 1729 are 1, 7, 13, 19, 91, 133, 247, 1729
The factors of 6065 are 1, 5, 1213, 6065
The HCF of 1729,6065 is 1.
Lets's calculate GCF of 1729,6065
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 1729,6065 By Matching Biggest Common Factor Method
Now, list down the factors of 1729
:1,7,13,19,91,133,247,1729
Now, list down the factors of 6065
:1,5,1213,6065
Greatest Common Factor
We found the factors 1729,6065 . The biggest common factor number is the GCF number.
So the greatest common factor 1729,6065 is 1.
Lets's calculate LCM of 420,7500
| 2 | 420, 7500 |
| 2 | 210, 3750 |
| 3 | 105, 1875 |
| 5 | 35, 625 |
| 7, 125 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 7 x 125 = 52500
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/52500
Therefore, the GCF of Fractions 1729/420,6065/7500 is 1/52500
Least Common Multiple of 420,7500 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 420,7500 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(420,7500) = 60
common factors(in case of two or more numbers have common factors) = 1
GCF(420,7500) x common factors =60 x 1 = 60
LCM(420,7500) = ( 420 × 7500 ) / 60
LCM(420,7500) = 3150000 / 60
LCM(420,7500) = 52500
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FAQs on GCF of Fractions of 1729/420, 6065/7500
1. What is the HCF of 1729,6065?
The HCF of 1729,6065 is 1
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 1729/420, 6065/7500?
Answer: GCF of Numerators as per given numbers 1729/420, 6065/7500 is
GCF of Numerators i.e. for 1729,6065 is 1
LCM of denominators i.e. for 420,7500 is 52500.
Thus, GCF of Fractions is 1/52500.Finally, GCF of Fractions for 1729/420, 6065/7500 is 1/52500.