GCF of 380/53, 320/675
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 380/53, 320/675 i.e 20/35775 easily. The following is the detailed procedure to determine the greatest common factor of fractions 380/53, 320/675.
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 380/53,320/675?
Given fractions are 380/53,320/675
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 380/53,320/675, numerators are 380,320
Denominators are 53,675
The GCF of 380,320 is 20 .
LCM of 53,675 is 35775.
The greatest common factor of 380/53,320/675 = [GCF of 380,320]/[LCM of 53,675]= 20/35775
Therefore, the GCF of 380/53,320/675 is 20/35775.
To find the highest common factor of 380,320, we have to find the factors of both numbers and list the highest common factor.
The factors of 380 are 1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380
The factors of 320 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 160, 320
The HCF of 380,320 is 20.
Lets's calculate GCF of 380,320
| 2 | 380, 320 |
| 2 | 190, 160 |
| 5 | 95, 80 |
| 19, 16 |
∴ So the GCF of the given numbers is 2 x 2 x 5 = 20
Greatest Common Factor of 380,320 By Matching Biggest Common Factor Method
Now, list down the factors of 380
:1,2,4,5,10,19,20,38,76,95,190,380
Now, list down the factors of 320
:1,2,4,5,8,10,16,20,32,40,64,80,160,320
Greatest Common Factor
We found the factors 380,320 . The biggest common factor number is the GCF number.
So the greatest common factor 380,320 is 20.
Lets's calculate LCM of 53,675
Given numbers has no common factors except 1. So, there LCM is their product i.e 35775
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 20/35775
Therefore, the GCF of Fractions 380/53,320/675 is 20/35775
Least Common Multiple of 53,675 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 53,675 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(53,675) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(53,675) x common factors =1 x 1 = 1
LCM(53,675) = ( 53 × 675 ) / 1
LCM(53,675) = 35775 / 1
LCM(53,675) = 35775
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FAQs on GCF of Fractions of 380/53, 320/675
1. What is the HCF of 380,320?
The HCF of 380,320 is 20
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 380/53, 320/675?
Answer: GCF of Numerators as per given numbers 380/53, 320/675 is
GCF of Numerators i.e. for 380,320 is 20
LCM of denominators i.e. for 53,675 is 35775.
Thus, GCF of Fractions is 20/35775.Finally, GCF of Fractions for 380/53, 320/675 is 20/35775.