GCF of 6700/310, 6540/6025
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6700/310, 6540/6025 i.e 20/373550 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6700/310, 6540/6025.
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 6700/310,6540/6025?
Given fractions are 6700/310,6540/6025
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 6700/310,6540/6025, numerators are 6700,6540
Denominators are 310,6025
The GCF of 6700,6540 is 20 .
LCM of 310,6025 is 373550.
The greatest common factor of 6700/310,6540/6025 = [GCF of 6700,6540]/[LCM of 310,6025]= 20/373550
Therefore, the GCF of 6700/310,6540/6025 is 20/373550.
To find the highest common factor of 6700,6540, we have to find the factors of both numbers and list the highest common factor.
The factors of 6700 are 1, 2, 4, 5, 10, 20, 25, 50, 67, 100, 134, 268, 335, 670, 1340, 1675, 3350, 6700
The factors of 6540 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60, 109, 218, 327, 436, 545, 654, 1090, 1308, 1635, 2180, 3270, 6540
The HCF of 6700,6540 is 20.
Lets's calculate GCF of 6700,6540
| 2 | 6700, 6540 |
| 2 | 3350, 3270 |
| 5 | 1675, 1635 |
| 335, 327 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Greatest Common Factor of 6700,6540 By Matching Biggest Common Factor Method
Now, list down the factors of 6700
:1,2,4,5,10,20,25,50,67,100,134,268,335,670,1340,1675,3350,6700
Now, list down the factors of 6540
:1,2,3,4,5,6,10,12,15,20,30,60,109,218,327,436,545,654,1090,1308,1635,2180,3270,6540
Greatest Common Factor
We found the factors 6700,6540 . The biggest common factor number is the GCF number.
So the greatest common factor 6700,6540 is 20.
Lets's calculate LCM of 310,6025
| 5 | 310, 6025 |
| 62, 1205 |
∴ So the LCM of the given numbers is 5 x 62 x 1205 = 373550
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/373550
Therefore, the GCF of Fractions 6700/310,6540/6025 is 20/373550
Least Common Multiple of 310,6025 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 310,6025 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(310,6025) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(310,6025) x common factors =5 x 1 = 5
LCM(310,6025) = ( 310 × 6025 ) / 5
LCM(310,6025) = 1867750 / 5
LCM(310,6025) = 373550
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FAQs on GCF of Fractions of 6700/310, 6540/6025
1. What is the HCF of 6700,6540?
The HCF of 6700,6540 is 20
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 6700/310, 6540/6025?
Answer: GCF of Numerators as per given numbers 6700/310, 6540/6025 is
GCF of Numerators i.e. for 6700,6540 is 20
LCM of denominators i.e. for 310,6025 is 373550.
Thus, GCF of Fractions is 20/373550.Finally, GCF of Fractions for 6700/310, 6540/6025 is 20/373550.