GCF of 360/81, 400/342
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 360/81, 400/342 i.e 40/3078 easily. The following is the detailed procedure to determine the greatest common factor of fractions 360/81, 400/342.
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 360/81,400/342?
Given fractions are 360/81,400/342
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 360/81,400/342, numerators are 360,400
Denominators are 81,342
The GCF of 360,400 is 40 .
LCM of 81,342 is 3078.
The greatest common factor of 360/81,400/342 = [GCF of 360,400]/[LCM of 81,342]= 40/3078
Therefore, the GCF of 360/81,400/342 is 40/3078.
To find the highest common factor of 360,400, we have to find the factors of both numbers and list the highest common factor.
The factors of 360 are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360
The factors of 400 are 1, 2, 4, 5, 8, 10, 16, 20, 25, 40, 50, 80, 100, 200, 400
The HCF of 360,400 is 40.
Lets's calculate GCF of 360,400
| 2 | 360, 400 |
| 2 | 180, 200 |
| 2 | 90, 100 |
| 5 | 45, 50 |
| 9, 10 |
∴ So the GCF of the given numbers is 2 x 2 x 2 x 5 = 40
Greatest Common Factor of 360,400 By Matching Biggest Common Factor Method
Now, list down the factors of 360
:1,2,3,4,5,6,8,9,10,12,15,18,20,24,30,36,40,45,60,72,90,120,180,360
Now, list down the factors of 400
:1,2,4,5,8,10,16,20,25,40,50,80,100,200,400
Greatest Common Factor
We found the factors 360,400 . The biggest common factor number is the GCF number.
So the greatest common factor 360,400 is 40.
Lets's calculate LCM of 81,342
| 3 | 81, 342 |
| 3 | 27, 114 |
| 9, 38 |
∴ So the LCM of the given numbers is 3 x 3 x 9 x 38 = 3078
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 40/3078
Therefore, the GCF of Fractions 360/81,400/342 is 40/3078
Least Common Multiple of 81,342 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 81,342 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(81,342) = 9
common factors(in case of two or more numbers have common factors) = 1
GCF(81,342) x common factors =9 x 1 = 9
LCM(81,342) = ( 81 × 342 ) / 9
LCM(81,342) = 27702 / 9
LCM(81,342) = 3078
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FAQs on GCF of Fractions of 360/81, 400/342
1. What is the HCF of 360,400?
The HCF of 360,400 is 40
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 360/81, 400/342?
Answer: GCF of Numerators as per given numbers 360/81, 400/342 is
GCF of Numerators i.e. for 360,400 is 40
LCM of denominators i.e. for 81,342 is 3078.
Thus, GCF of Fractions is 40/3078.Finally, GCF of Fractions for 360/81, 400/342 is 40/3078.