GCF of 1204/740, 8686/814
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 1204/740, 8686/814 i.e 86/8140 easily. The following is the detailed procedure to determine the greatest common factor of fractions 1204/740, 8686/814.
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 1204/740,8686/814?
Given fractions are 1204/740,8686/814
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 1204/740,8686/814, numerators are 1204,8686
Denominators are 740,814
The GCF of 1204,8686 is 86 .
LCM of 740,814 is 8140.
The greatest common factor of 1204/740,8686/814 = [GCF of 1204,8686]/[LCM of 740,814]= 86/8140
Therefore, the GCF of 1204/740,8686/814 is 86/8140.
To find the highest common factor of 1204,8686, we have to find the factors of both numbers and list the highest common factor.
The factors of 1204 are 1, 2, 4, 7, 14, 28, 43, 86, 172, 301, 602, 1204
The factors of 8686 are 1, 2, 43, 86, 101, 202, 4343, 8686
The HCF of 1204,8686 is 86.
Lets's calculate GCF of 1204,8686
| 2 | 1204, 8686 |
| 43 | 602, 4343 |
| 14, 101 |
∴ So the GCF of the given numbers is 2 x 43 = 86
Greatest Common Factor of 1204,8686 By Matching Biggest Common Factor Method
Now, list down the factors of 1204
:1,2,4,7,14,28,43,86,172,301,602,1204
Now, list down the factors of 8686
:1,2,43,86,101,202,4343,8686
Greatest Common Factor
We found the factors 1204,8686 . The biggest common factor number is the GCF number.
So the greatest common factor 1204,8686 is 86.
Lets's calculate LCM of 740,814
| 2 | 740, 814 |
| 37 | 370, 407 |
| 10, 11 |
∴ So the LCM of the given numbers is 2 x 37 x 10 x 11 = 8140
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 86/8140
Therefore, the GCF of Fractions 1204/740,8686/814 is 86/8140
Least Common Multiple of 740,814 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 740,814 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(740,814) = 74
common factors(in case of two or more numbers have common factors) = 1
GCF(740,814) x common factors =74 x 1 = 74
LCM(740,814) = ( 740 × 814 ) / 74
LCM(740,814) = 602360 / 74
LCM(740,814) = 8140
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FAQs on GCF of Fractions of 1204/740, 8686/814
1. What is the HCF of 1204,8686?
The HCF of 1204,8686 is 86
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 1204/740, 8686/814?
Answer: GCF of Numerators as per given numbers 1204/740, 8686/814 is
GCF of Numerators i.e. for 1204,8686 is 86
LCM of denominators i.e. for 740,814 is 8140.
Thus, GCF of Fractions is 86/8140.Finally, GCF of Fractions for 1204/740, 8686/814 is 86/8140.