GCF of 2905/314, 8176/620
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2905/314, 8176/620 i.e 7/97340 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2905/314, 8176/620.
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 2905/314,8176/620?
Given fractions are 2905/314,8176/620
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 2905/314,8176/620, numerators are 2905,8176
Denominators are 314,620
The GCF of 2905,8176 is 7 .
LCM of 314,620 is 97340.
The greatest common factor of 2905/314,8176/620 = [GCF of 2905,8176]/[LCM of 314,620]= 7/97340
Therefore, the GCF of 2905/314,8176/620 is 7/97340.
To find the highest common factor of 2905,8176, we have to find the factors of both numbers and list the highest common factor.
The factors of 2905 are 1, 5, 7, 35, 83, 415, 581, 2905
The factors of 8176 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 73, 112, 146, 292, 511, 584, 1022, 1168, 2044, 4088, 8176
The HCF of 2905,8176 is 7.
Lets's calculate GCF of 2905,8176
| 7 | 2905, 8176 |
| 415, 1168 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 2905,8176 By Matching Biggest Common Factor Method
Now, list down the factors of 2905
:1,5,7,35,83,415,581,2905
Now, list down the factors of 8176
:1,2,4,7,8,14,16,28,56,73,112,146,292,511,584,1022,1168,2044,4088,8176
Greatest Common Factor
We found the factors 2905,8176 . The biggest common factor number is the GCF number.
So the greatest common factor 2905,8176 is 7.
Lets's calculate LCM of 314,620
| 2 | 314, 620 |
| 157, 310 |
∴ So the LCM of the given numbers is 2 x 157 x 310 = 97340
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/97340
Therefore, the GCF of Fractions 2905/314,8176/620 is 7/97340
Least Common Multiple of 314,620 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 314,620 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(314,620) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(314,620) x common factors =2 x 1 = 2
LCM(314,620) = ( 314 × 620 ) / 2
LCM(314,620) = 194680 / 2
LCM(314,620) = 97340
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FAQs on GCF of Fractions of 2905/314, 8176/620
1. What is the HCF of 2905,8176?
The HCF of 2905,8176 is 7
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 2905/314, 8176/620?
Answer: GCF of Numerators as per given numbers 2905/314, 8176/620 is
GCF of Numerators i.e. for 2905,8176 is 7
LCM of denominators i.e. for 314,620 is 97340.
Thus, GCF of Fractions is 7/97340.Finally, GCF of Fractions for 2905/314, 8176/620 is 7/97340.