GCF of 856/205, 312/875
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 856/205, 312/875 i.e 8/35875 easily. The following is the detailed procedure to determine the greatest common factor of fractions 856/205, 312/875.
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 856/205,312/875?
Given fractions are 856/205,312/875
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 856/205,312/875, numerators are 856,312
Denominators are 205,875
The GCF of 856,312 is 8 .
LCM of 205,875 is 35875.
The greatest common factor of 856/205,312/875 = [GCF of 856,312]/[LCM of 205,875]= 8/35875
Therefore, the GCF of 856/205,312/875 is 8/35875.
To find the highest common factor of 856,312, we have to find the factors of both numbers and list the highest common factor.
The factors of 856 are 1, 2, 4, 8, 107, 214, 428, 856
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 856,312 is 8.
Lets's calculate GCF of 856,312
| 2 | 856, 312 |
| 2 | 428, 156 |
| 2 | 214, 78 |
| 107, 39 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Greatest Common Factor of 856,312 By Matching Biggest Common Factor Method
Now, list down the factors of 856
:1,2,4,8,107,214,428,856
Now, list down the factors of 312
:1,2,3,4,6,8,12,13,24,26,39,52,78,104,156,312
Greatest Common Factor
We found the factors 856,312 . The biggest common factor number is the GCF number.
So the greatest common factor 856,312 is 8.
Lets's calculate LCM of 205,875
| 5 | 205, 875 |
| 41, 175 |
∴ So the LCM of the given numbers is 5 x 41 x 175 = 35875
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/35875
Therefore, the GCF of Fractions 856/205,312/875 is 8/35875
Least Common Multiple of 205,875 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 205,875 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(205,875) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(205,875) x common factors =5 x 1 = 5
LCM(205,875) = ( 205 × 875 ) / 5
LCM(205,875) = 179375 / 5
LCM(205,875) = 35875
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 856/205, 312/875
1. What is the HCF of 856,312?
The HCF of 856,312 is 8
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 856/205, 312/875?
Answer: GCF of Numerators as per given numbers 856/205, 312/875 is
GCF of Numerators i.e. for 856,312 is 8
LCM of denominators i.e. for 205,875 is 35875.
Thus, GCF of Fractions is 8/35875.Finally, GCF of Fractions for 856/205, 312/875 is 8/35875.