GCF of 1540/406, 6413/362
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1540/406, 6413/362 i.e 11/73486 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1540/406, 6413/362.
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 1540/406,6413/362?
Given fractions are 1540/406,6413/362
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 1540/406,6413/362, numerators are 1540,6413
Denominators are 406,362
The GCF of 1540,6413 is 11 .
LCM of 406,362 is 73486.
The greatest common factor of 1540/406,6413/362 = [GCF of 1540,6413]/[LCM of 406,362]= 11/73486
Therefore, the GCF of 1540/406,6413/362 is 11/73486.
To find the highest common factor of 1540,6413, we have to find the factors of both numbers and list the highest common factor.
The factors of 1540 are 1, 2, 4, 5, 7, 10, 11, 14, 20, 22, 28, 35, 44, 55, 70, 77, 110, 140, 154, 220, 308, 385, 770, 1540
The factors of 6413 are 1, 11, 53, 121, 583, 6413
The HCF of 1540,6413 is 11.
Lets's calculate GCF of 1540,6413
| 11 | 1540, 6413 |
| 140, 583 |
∴ So the GCF of the given numbers is 11 = 11
Greatest Common Factor of 1540,6413 By Matching Biggest Common Factor Method
Now, list down the factors of 1540
:1,2,4,5,7,10,11,14,20,22,28,35,44,55,70,77,110,140,154,220,308,385,770,1540
Now, list down the factors of 6413
:1,11,53,121,583,6413
Greatest Common Factor
We found the factors 1540,6413 . The biggest common factor number is the GCF number.
So the greatest common factor 1540,6413 is 11.
Lets's calculate LCM of 406,362
| 2 | 406, 362 |
| 203, 181 |
∴ So the LCM of the given numbers is 2 x 203 x 181 = 73486
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 11/73486
Therefore, the GCF of Fractions 1540/406,6413/362 is 11/73486
Least Common Multiple of 406,362 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 406,362 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(406,362) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(406,362) x common factors =2 x 1 = 2
LCM(406,362) = ( 406 × 362 ) / 2
LCM(406,362) = 146972 / 2
LCM(406,362) = 73486
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FAQs on GCF of Fractions of 1540/406, 6413/362
1. What is the HCF of 1540,6413?
The HCF of 1540,6413 is 11
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 1540/406, 6413/362?
Answer: GCF of Numerators as per given numbers 1540/406, 6413/362 is
GCF of Numerators i.e. for 1540,6413 is 11
LCM of denominators i.e. for 406,362 is 73486.
Thus, GCF of Fractions is 11/73486.Finally, GCF of Fractions for 1540/406, 6413/362 is 11/73486.