GCF of 804/149, 8164/214
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 804/149, 8164/214 i.e 4/31886 easily. The following is the detailed procedure to determine the greatest common factor of fractions 804/149, 8164/214.
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 804/149,8164/214?
Given fractions are 804/149,8164/214
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 804/149,8164/214, numerators are 804,8164
Denominators are 149,214
The GCF of 804,8164 is 4 .
LCM of 149,214 is 31886.
The greatest common factor of 804/149,8164/214 = [GCF of 804,8164]/[LCM of 149,214]= 4/31886
Therefore, the GCF of 804/149,8164/214 is 4/31886.
To find the highest common factor of 804,8164, we have to find the factors of both numbers and list the highest common factor.
The factors of 804 are 1, 2, 3, 4, 6, 12, 67, 134, 201, 268, 402, 804
The factors of 8164 are 1, 2, 4, 13, 26, 52, 157, 314, 628, 2041, 4082, 8164
The HCF of 804,8164 is 4.
Lets's calculate GCF of 804,8164
| 2 | 804, 8164 |
| 2 | 402, 4082 |
| 201, 2041 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 804,8164 By Matching Biggest Common Factor Method
Now, list down the factors of 804
:1,2,3,4,6,12,67,134,201,268,402,804
Now, list down the factors of 8164
:1,2,4,13,26,52,157,314,628,2041,4082,8164
Greatest Common Factor
We found the factors 804,8164 . The biggest common factor number is the GCF number.
So the greatest common factor 804,8164 is 4.
Lets's calculate LCM of 149,214
Given numbers has no common factors except 1. So, there LCM is their product i.e 31886
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/31886
Therefore, the GCF of Fractions 804/149,8164/214 is 4/31886
Least Common Multiple of 149,214 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 149,214 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(149,214) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(149,214) x common factors =1 x 1 = 1
LCM(149,214) = ( 149 × 214 ) / 1
LCM(149,214) = 31886 / 1
LCM(149,214) = 31886
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FAQs on GCF of Fractions of 804/149, 8164/214
1. What is the HCF of 804,8164?
The HCF of 804,8164 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 804/149, 8164/214?
Answer: GCF of Numerators as per given numbers 804/149, 8164/214 is
GCF of Numerators i.e. for 804,8164 is 4
LCM of denominators i.e. for 149,214 is 31886.
Thus, GCF of Fractions is 4/31886.Finally, GCF of Fractions for 804/149, 8164/214 is 4/31886.