GCF of 510/382, 490/400
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 510/382, 490/400 i.e 10/76400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 510/382, 490/400.
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 510/382,490/400?
Given fractions are 510/382,490/400
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 510/382,490/400, numerators are 510,490
Denominators are 382,400
The GCF of 510,490 is 10 .
LCM of 382,400 is 76400.
The greatest common factor of 510/382,490/400 = [GCF of 510,490]/[LCM of 382,400]= 10/76400
Therefore, the GCF of 510/382,490/400 is 10/76400.
To find the highest common factor of 510,490, we have to find the factors of both numbers and list the highest common factor.
The factors of 510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 102, 170, 255, 510
The factors of 490 are 1, 2, 5, 7, 10, 14, 35, 49, 70, 98, 245, 490
The HCF of 510,490 is 10.
Lets's calculate GCF of 510,490
| 2 | 510, 490 |
| 5 | 255, 245 |
| 51, 49 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 510,490 By Matching Biggest Common Factor Method
Now, list down the factors of 510
:1,2,3,5,6,10,15,17,30,34,51,85,102,170,255,510
Now, list down the factors of 490
:1,2,5,7,10,14,35,49,70,98,245,490
Greatest Common Factor
We found the factors 510,490 . The biggest common factor number is the GCF number.
So the greatest common factor 510,490 is 10.
Lets's calculate LCM of 382,400
| 2 | 382, 400 |
| 191, 200 |
∴ So the LCM of the given numbers is 2 x 191 x 200 = 76400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/76400
Therefore, the GCF of Fractions 510/382,490/400 is 10/76400
Least Common Multiple of 382,400 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 382,400 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(382,400) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(382,400) x common factors =2 x 1 = 2
LCM(382,400) = ( 382 × 400 ) / 2
LCM(382,400) = 152800 / 2
LCM(382,400) = 76400
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FAQs on GCF of Fractions of 510/382, 490/400
1. What is the HCF of 510,490?
The HCF of 510,490 is 10
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 510/382, 490/400?
Answer: GCF of Numerators as per given numbers 510/382, 490/400 is
GCF of Numerators i.e. for 510,490 is 10
LCM of denominators i.e. for 382,400 is 76400.
Thus, GCF of Fractions is 10/76400.Finally, GCF of Fractions for 510/382, 490/400 is 10/76400.