GCF of 506/400, 8029/315
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 506/400, 8029/315 i.e 1/25200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 506/400, 8029/315.
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 506/400,8029/315?
Given fractions are 506/400,8029/315
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 506/400,8029/315, numerators are 506,8029
Denominators are 400,315
The GCF of 506,8029 is 1 .
LCM of 400,315 is 25200.
The greatest common factor of 506/400,8029/315 = [GCF of 506,8029]/[LCM of 400,315]= 1/25200
Therefore, the GCF of 506/400,8029/315 is 1/25200.
To find the highest common factor of 506,8029, we have to find the factors of both numbers and list the highest common factor.
The factors of 506 are 1, 2, 11, 22, 23, 46, 253, 506
The factors of 8029 are 1, 7, 31, 37, 217, 259, 1147, 8029
The HCF of 506,8029 is 1.
Lets's calculate GCF of 506,8029
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 506,8029 By Matching Biggest Common Factor Method
Now, list down the factors of 506
:1,2,11,22,23,46,253,506
Now, list down the factors of 8029
:1,7,31,37,217,259,1147,8029
Greatest Common Factor
We found the factors 506,8029 . The biggest common factor number is the GCF number.
So the greatest common factor 506,8029 is 1.
Lets's calculate LCM of 400,315
| 5 | 400, 315 |
| 80, 63 |
∴ So the LCM of the given numbers is 5 x 80 x 63 = 25200
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/25200
Therefore, the GCF of Fractions 506/400,8029/315 is 1/25200
Least Common Multiple of 400,315 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 400,315 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(400,315) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(400,315) x common factors =5 x 1 = 5
LCM(400,315) = ( 400 × 315 ) / 5
LCM(400,315) = 126000 / 5
LCM(400,315) = 25200
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FAQs on GCF of Fractions of 506/400, 8029/315
1. What is the HCF of 506,8029?
The HCF of 506,8029 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 506/400, 8029/315?
Answer: GCF of Numerators as per given numbers 506/400, 8029/315 is
GCF of Numerators i.e. for 506,8029 is 1
LCM of denominators i.e. for 400,315 is 25200.
Thus, GCF of Fractions is 1/25200.Finally, GCF of Fractions for 506/400, 8029/315 is 1/25200.