GCF of 7907/820, 1658/678
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7907/820, 1658/678 i.e 1/277980 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7907/820, 1658/678.
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 7907/820,1658/678?
Given fractions are 7907/820,1658/678
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 7907/820,1658/678, numerators are 7907,1658
Denominators are 820,678
The GCF of 7907,1658 is 1 .
LCM of 820,678 is 277980.
The greatest common factor of 7907/820,1658/678 = [GCF of 7907,1658]/[LCM of 820,678]= 1/277980
Therefore, the GCF of 7907/820,1658/678 is 1/277980.
To find the highest common factor of 7907,1658, we have to find the factors of both numbers and list the highest common factor.
The factors of 7907 are 1, 7907
The factors of 1658 are 1, 2, 829, 1658
The HCF of 7907,1658 is 1.
Lets's calculate GCF of 7907,1658
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 7907,1658 By Matching Biggest Common Factor Method
Now, list down the factors of 7907
:1,7907
Now, list down the factors of 1658
:1,2,829,1658
Greatest Common Factor
We found the factors 7907,1658 . The biggest common factor number is the GCF number.
So the greatest common factor 7907,1658 is 1.
Lets's calculate LCM of 820,678
| 2 | 820, 678 |
| 410, 339 |
∴ So the LCM of the given numbers is 2 x 410 x 339 = 277980
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/277980
Therefore, the GCF of Fractions 7907/820,1658/678 is 1/277980
Least Common Multiple of 820,678 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 820,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(820,678) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(820,678) x common factors =2 x 1 = 2
LCM(820,678) = ( 820 × 678 ) / 2
LCM(820,678) = 555960 / 2
LCM(820,678) = 277980
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FAQs on GCF of Fractions of 7907/820, 1658/678
1. What is the HCF of 7907,1658?
The HCF of 7907,1658 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 7907/820, 1658/678?
Answer: GCF of Numerators as per given numbers 7907/820, 1658/678 is
GCF of Numerators i.e. for 7907,1658 is 1
LCM of denominators i.e. for 820,678 is 277980.
Thus, GCF of Fractions is 1/277980.Finally, GCF of Fractions for 7907/820, 1658/678 is 1/277980.