GCF of 7673/320, 7678/8174
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7673/320, 7678/8174 i.e 1/1307840 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7673/320, 7678/8174.
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 7673/320,7678/8174?
Given fractions are 7673/320,7678/8174
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 7673/320,7678/8174, numerators are 7673,7678
Denominators are 320,8174
The GCF of 7673,7678 is 1 .
LCM of 320,8174 is 1307840.
The greatest common factor of 7673/320,7678/8174 = [GCF of 7673,7678]/[LCM of 320,8174]= 1/1307840
Therefore, the GCF of 7673/320,7678/8174 is 1/1307840.
To find the highest common factor of 7673,7678, we have to find the factors of both numbers and list the highest common factor.
The factors of 7673 are 1, 7673
The factors of 7678 are 1, 2, 11, 22, 349, 698, 3839, 7678
The HCF of 7673,7678 is 1.
Lets's calculate GCF of 7673,7678
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 7673,7678 By Matching Biggest Common Factor Method
Now, list down the factors of 7673
:1,7673
Now, list down the factors of 7678
:1,2,11,22,349,698,3839,7678
Greatest Common Factor
We found the factors 7673,7678 . The biggest common factor number is the GCF number.
So the greatest common factor 7673,7678 is 1.
Lets's calculate LCM of 320,8174
| 2 | 320, 8174 |
| 160, 4087 |
∴ So the LCM of the given numbers is 2 x 160 x 4087 = 1307840
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1307840
Therefore, the GCF of Fractions 7673/320,7678/8174 is 1/1307840
Least Common Multiple of 320,8174 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 320,8174 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(320,8174) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(320,8174) x common factors =2 x 1 = 2
LCM(320,8174) = ( 320 × 8174 ) / 2
LCM(320,8174) = 2615680 / 2
LCM(320,8174) = 1307840
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FAQs on GCF of Fractions of 7673/320, 7678/8174
1. What is the HCF of 7673,7678?
The HCF of 7673,7678 is 1
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 7673/320, 7678/8174?
Answer: GCF of Numerators as per given numbers 7673/320, 7678/8174 is
GCF of Numerators i.e. for 7673,7678 is 1
LCM of denominators i.e. for 320,8174 is 1307840.
Thus, GCF of Fractions is 1/1307840.Finally, GCF of Fractions for 7673/320, 7678/8174 is 1/1307840.