GCF of 7341/282, 5976/8960
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7341/282, 5976/8960 i.e 3/1263360 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7341/282, 5976/8960.
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 7341/282,5976/8960?
Given fractions are 7341/282,5976/8960
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 7341/282,5976/8960, numerators are 7341,5976
Denominators are 282,8960
The GCF of 7341,5976 is 3 .
LCM of 282,8960 is 1263360.
The greatest common factor of 7341/282,5976/8960 = [GCF of 7341,5976]/[LCM of 282,8960]= 3/1263360
Therefore, the GCF of 7341/282,5976/8960 is 3/1263360.
To find the highest common factor of 7341,5976, we have to find the factors of both numbers and list the highest common factor.
The factors of 7341 are 1, 3, 2447, 7341
The factors of 5976 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72, 83, 166, 249, 332, 498, 664, 747, 996, 1494, 1992, 2988, 5976
The HCF of 7341,5976 is 3.
Lets's calculate GCF of 7341,5976
| 3 | 7341, 5976 |
| 2447, 1992 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 7341,5976 By Matching Biggest Common Factor Method
Now, list down the factors of 7341
:1,3,2447,7341
Now, list down the factors of 5976
:1,2,3,4,6,8,9,12,18,24,36,72,83,166,249,332,498,664,747,996,1494,1992,2988,5976
Greatest Common Factor
We found the factors 7341,5976 . The biggest common factor number is the GCF number.
So the greatest common factor 7341,5976 is 3.
Lets's calculate LCM of 282,8960
| 2 | 282, 8960 |
| 141, 4480 |
∴ So the LCM of the given numbers is 2 x 141 x 4480 = 1263360
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1263360
Therefore, the GCF of Fractions 7341/282,5976/8960 is 3/1263360
Least Common Multiple of 282,8960 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 282,8960 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(282,8960) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(282,8960) x common factors =2 x 1 = 2
LCM(282,8960) = ( 282 × 8960 ) / 2
LCM(282,8960) = 2526720 / 2
LCM(282,8960) = 1263360
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FAQs on GCF of Fractions of 7341/282, 5976/8960
1. What is the HCF of 7341,5976?
The HCF of 7341,5976 is 3
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 7341/282, 5976/8960?
Answer: GCF of Numerators as per given numbers 7341/282, 5976/8960 is
GCF of Numerators i.e. for 7341,5976 is 3
LCM of denominators i.e. for 282,8960 is 1263360.
Thus, GCF of Fractions is 3/1263360.Finally, GCF of Fractions for 7341/282, 5976/8960 is 3/1263360.