GCF of 3/40, 37/64, 80/356, 322/200
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3/40, 37/64, 80/356, 322/200 i.e 1/142400 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3/40, 37/64, 80/356, 322/200.
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 3/40,37/64,80/356,322/200?
Given fractions are 3/40,37/64,80/356,322/200
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 3/40,37/64,80/356,322/200, numerators are 3,37,80,322
Denominators are 40,64,356,200
The GCF of 3,37,80,322 is 1 .
LCM of 40,64,356,200 is 142400.
The greatest common factor of 3/40,37/64,80/356,322/200 = [GCF of 3,37,80,322]/[LCM of 40,64,356,200]= 1/142400
Therefore, the GCF of 3/40,37/64,80/356,322/200 is 1/142400.
To find the highest common factor of 3,37,80,322, we have to find the factors of both numbers and list the highest common factor.
The factors of 3 are 1, 3
The factors of 37 are 1, 37
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
The factors of 322 are 1, 2, 7, 14, 23, 46, 161, 322
The HCF of 3,37,80,322 is 1.
Lets's calculate GCF of 3,37,80,322
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 3,37,80,322 By Matching Biggest Common Factor Method
Now, list down the factors of 3
:1,3
Now, list down the factors of 37
:1,37
Now, list down the factors of 80
:1,2,4,5,8,10,16,20,40,80
Now, list down the factors of 322
:1,2,7,14,23,46,161,322
Greatest Common Factor
We found the factors 3,37,80,322 . The biggest common factor number is the GCF number.
So the greatest common factor 3,37,80,322 is 1.
Lets's calculate LCM of 40,64,356,200
| 2 | 40, 64, 356, 200 |
| 2 | 20, 32, 178, 100 |
| 2 | 10, 16, 89, 50 |
| 5 | 5, 8, 89, 25 |
| 1, 8, 89, 5 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 5 x 1 x 8 x 89 x 5 = 142400
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/142400
Therefore, the GCF of Fractions 3/40,37/64,80/356,322/200 is 1/142400
Least Common Multiple of 40,64,356,200 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 40,64,356,200 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(40,64,356,200) = 4
common factors(in case of two or more numbers have common factors) = 320
GCF(40,64,356,200) x common factors =4 x 320 = 1280
LCM(40,64,356,200) = ( 40 × 64 × 356 × 200 ) / 1280
LCM(40,64,356,200) = 182272000 / 1280
LCM(40,64,356,200) = 142400
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 3/40, 37/64, 80/356, 322/200
1. What is the HCF of 3,37,80,322?
The HCF of 3,37,80,322 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 3/40, 37/64, 80/356, 322/200?
Answer: GCF of Numerators as per given numbers 3/40, 37/64, 80/356, 322/200 is
GCF of Numerators i.e. for 3,37,80,322 is 1
LCM of denominators i.e. for 40,64,356,200 is 142400.
Thus, GCF of Fractions is 1/142400.Finally, GCF of Fractions for 3/40, 37/64, 80/356, 322/200 is 1/142400.