GCF of 6486/974, 6978/7066
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6486/974, 6978/7066 i.e 6/3441142 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6486/974, 6978/7066.
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 6486/974,6978/7066?
Given fractions are 6486/974,6978/7066
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 6486/974,6978/7066, numerators are 6486,6978
Denominators are 974,7066
The GCF of 6486,6978 is 6 .
LCM of 974,7066 is 3441142.
The greatest common factor of 6486/974,6978/7066 = [GCF of 6486,6978]/[LCM of 974,7066]= 6/3441142
Therefore, the GCF of 6486/974,6978/7066 is 6/3441142.
To find the highest common factor of 6486,6978, we have to find the factors of both numbers and list the highest common factor.
The factors of 6486 are 1, 2, 3, 6, 23, 46, 47, 69, 94, 138, 141, 282, 1081, 2162, 3243, 6486
The factors of 6978 are 1, 2, 3, 6, 1163, 2326, 3489, 6978
The HCF of 6486,6978 is 6.
Lets's calculate GCF of 6486,6978
| 2 | 6486, 6978 |
| 3 | 3243, 3489 |
| 1081, 1163 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 6486,6978 By Matching Biggest Common Factor Method
Now, list down the factors of 6486
:1,2,3,6,23,46,47,69,94,138,141,282,1081,2162,3243,6486
Now, list down the factors of 6978
:1,2,3,6,1163,2326,3489,6978
Greatest Common Factor
We found the factors 6486,6978 . The biggest common factor number is the GCF number.
So the greatest common factor 6486,6978 is 6.
Lets's calculate LCM of 974,7066
| 2 | 974, 7066 |
| 487, 3533 |
∴ So the LCM of the given numbers is 2 x 487 x 3533 = 3441142
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/3441142
Therefore, the GCF of Fractions 6486/974,6978/7066 is 6/3441142
Least Common Multiple of 974,7066 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 974,7066 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(974,7066) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(974,7066) x common factors =2 x 1 = 2
LCM(974,7066) = ( 974 × 7066 ) / 2
LCM(974,7066) = 6882284 / 2
LCM(974,7066) = 3441142
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FAQs on GCF of Fractions of 6486/974, 6978/7066
1. What is the HCF of 6486,6978?
The HCF of 6486,6978 is 6
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 6486/974, 6978/7066?
Answer: GCF of Numerators as per given numbers 6486/974, 6978/7066 is
GCF of Numerators i.e. for 6486,6978 is 6
LCM of denominators i.e. for 974,7066 is 3441142.
Thus, GCF of Fractions is 6/3441142.Finally, GCF of Fractions for 6486/974, 6978/7066 is 6/3441142.