GCF of 807/892, 312/814
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 807/892, 312/814 i.e 3/363044 easily. The following is the detailed procedure to determine the greatest common factor of fractions 807/892, 312/814.
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 807/892,312/814?
Given fractions are 807/892,312/814
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 807/892,312/814, numerators are 807,312
Denominators are 892,814
The GCF of 807,312 is 3 .
LCM of 892,814 is 363044.
The greatest common factor of 807/892,312/814 = [GCF of 807,312]/[LCM of 892,814]= 3/363044
Therefore, the GCF of 807/892,312/814 is 3/363044.
To find the highest common factor of 807,312, we have to find the factors of both numbers and list the highest common factor.
The factors of 807 are 1, 3, 269, 807
The factors of 312 are 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
The HCF of 807,312 is 3.
Lets's calculate GCF of 807,312
| 3 | 807, 312 |
| 269, 104 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 807,312 By Matching Biggest Common Factor Method
Now, list down the factors of 807
:1,3,269,807
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 807,312 . The biggest common factor number is the GCF number.
So the greatest common factor 807,312 is 3.
Lets's calculate LCM of 892,814
| 2 | 892, 814 |
| 446, 407 |
∴ So the LCM of the given numbers is 2 x 446 x 407 = 363044
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/363044
Therefore, the GCF of Fractions 807/892,312/814 is 3/363044
Least Common Multiple of 892,814 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 892,814 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(892,814) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(892,814) x common factors =2 x 1 = 2
LCM(892,814) = ( 892 × 814 ) / 2
LCM(892,814) = 726088 / 2
LCM(892,814) = 363044
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FAQs on GCF of Fractions of 807/892, 312/814
1. What is the HCF of 807,312?
The HCF of 807,312 is 3
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 807/892, 312/814?
Answer: GCF of Numerators as per given numbers 807/892, 312/814 is
GCF of Numerators i.e. for 807,312 is 3
LCM of denominators i.e. for 892,814 is 363044.
Thus, GCF of Fractions is 3/363044.Finally, GCF of Fractions for 807/892, 312/814 is 3/363044.