GCF of 828/854, 508/315
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 828/854, 508/315 i.e 4/38430 easily. The following is the detailed procedure to determine the greatest common factor of fractions 828/854, 508/315.
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 828/854,508/315?
Given fractions are 828/854,508/315
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 828/854,508/315, numerators are 828,508
Denominators are 854,315
The GCF of 828,508 is 4 .
LCM of 854,315 is 38430.
The greatest common factor of 828/854,508/315 = [GCF of 828,508]/[LCM of 854,315]= 4/38430
Therefore, the GCF of 828/854,508/315 is 4/38430.
To find the highest common factor of 828,508, we have to find the factors of both numbers and list the highest common factor.
The factors of 828 are 1, 2, 3, 4, 6, 9, 12, 18, 23, 36, 46, 69, 92, 138, 207, 276, 414, 828
The factors of 508 are 1, 2, 4, 127, 254, 508
The HCF of 828,508 is 4.
Lets's calculate GCF of 828,508
| 2 | 828, 508 |
| 2 | 414, 254 |
| 207, 127 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 828,508 By Matching Biggest Common Factor Method
Now, list down the factors of 828
:1,2,3,4,6,9,12,18,23,36,46,69,92,138,207,276,414,828
Now, list down the factors of 508
:1,2,4,127,254,508
Greatest Common Factor
We found the factors 828,508 . The biggest common factor number is the GCF number.
So the greatest common factor 828,508 is 4.
Lets's calculate LCM of 854,315
| 7 | 854, 315 |
| 122, 45 |
∴ So the LCM of the given numbers is 7 x 122 x 45 = 38430
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/38430
Therefore, the GCF of Fractions 828/854,508/315 is 4/38430
Least Common Multiple of 854,315 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 854,315 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(854,315) = 7
common factors(in case of two or more numbers have common factors) = 1
GCF(854,315) x common factors =7 x 1 = 7
LCM(854,315) = ( 854 × 315 ) / 7
LCM(854,315) = 269010 / 7
LCM(854,315) = 38430
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FAQs on GCF of Fractions of 828/854, 508/315
1. What is the HCF of 828,508?
The HCF of 828,508 is 4
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 828/854, 508/315?
Answer: GCF of Numerators as per given numbers 828/854, 508/315 is
GCF of Numerators i.e. for 828,508 is 4
LCM of denominators i.e. for 854,315 is 38430.
Thus, GCF of Fractions is 4/38430.Finally, GCF of Fractions for 828/854, 508/315 is 4/38430.