GCF of 3078/422, 3232/9764
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3078/422, 3232/9764 i.e 2/2060204 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3078/422, 3232/9764.
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 3078/422,3232/9764?
Given fractions are 3078/422,3232/9764
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 3078/422,3232/9764, numerators are 3078,3232
Denominators are 422,9764
The GCF of 3078,3232 is 2 .
LCM of 422,9764 is 2060204.
The greatest common factor of 3078/422,3232/9764 = [GCF of 3078,3232]/[LCM of 422,9764]= 2/2060204
Therefore, the GCF of 3078/422,3232/9764 is 2/2060204.
To find the highest common factor of 3078,3232, we have to find the factors of both numbers and list the highest common factor.
The factors of 3078 are 1, 2, 3, 6, 9, 18, 19, 27, 38, 54, 57, 81, 114, 162, 171, 342, 513, 1026, 1539, 3078
The factors of 3232 are 1, 2, 4, 8, 16, 32, 101, 202, 404, 808, 1616, 3232
The HCF of 3078,3232 is 2.
Lets's calculate GCF of 3078,3232
| 2 | 3078, 3232 |
| 1539, 1616 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 3078,3232 By Matching Biggest Common Factor Method
Now, list down the factors of 3078
:1,2,3,6,9,18,19,27,38,54,57,81,114,162,171,342,513,1026,1539,3078
Now, list down the factors of 3232
:1,2,4,8,16,32,101,202,404,808,1616,3232
Greatest Common Factor
We found the factors 3078,3232 . The biggest common factor number is the GCF number.
So the greatest common factor 3078,3232 is 2.
Lets's calculate LCM of 422,9764
| 2 | 422, 9764 |
| 211, 4882 |
∴ So the LCM of the given numbers is 2 x 211 x 4882 = 2060204
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2060204
Therefore, the GCF of Fractions 3078/422,3232/9764 is 2/2060204
Least Common Multiple of 422,9764 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 422,9764 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(422,9764) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(422,9764) x common factors =2 x 1 = 2
LCM(422,9764) = ( 422 × 9764 ) / 2
LCM(422,9764) = 4120408 / 2
LCM(422,9764) = 2060204
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FAQs on GCF of Fractions of 3078/422, 3232/9764
1. What is the HCF of 3078,3232?
The HCF of 3078,3232 is 2
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 3078/422, 3232/9764?
Answer: GCF of Numerators as per given numbers 3078/422, 3232/9764 is
GCF of Numerators i.e. for 3078,3232 is 2
LCM of denominators i.e. for 422,9764 is 2060204.
Thus, GCF of Fractions is 2/2060204.Finally, GCF of Fractions for 3078/422, 3232/9764 is 2/2060204.