GCF of 355/380, 420/575
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 355/380, 420/575 i.e 5/43700 easily. The following is the detailed procedure to determine the greatest common factor of fractions 355/380, 420/575.
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 355/380,420/575?
Given fractions are 355/380,420/575
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 355/380,420/575, numerators are 355,420
Denominators are 380,575
The GCF of 355,420 is 5 .
LCM of 380,575 is 43700.
The greatest common factor of 355/380,420/575 = [GCF of 355,420]/[LCM of 380,575]= 5/43700
Therefore, the GCF of 355/380,420/575 is 5/43700.
To find the highest common factor of 355,420, we have to find the factors of both numbers and list the highest common factor.
The factors of 355 are 1, 5, 71, 355
The factors of 420 are 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
The HCF of 355,420 is 5.
Lets's calculate GCF of 355,420
| 5 | 355, 420 |
| 71, 84 |
∴ So the GCF of the given numbers is 5 = 5
Greatest Common Factor of 355,420 By Matching Biggest Common Factor Method
Now, list down the factors of 355
:1,5,71,355
Now, list down the factors of 420
:1,2,3,4,5,6,7,10,12,14,15,20,21,28,30,35,42,60,70,84,105,140,210,420
Greatest Common Factor
We found the factors 355,420 . The biggest common factor number is the GCF number.
So the greatest common factor 355,420 is 5.
Lets's calculate LCM of 380,575
| 5 | 380, 575 |
| 76, 115 |
∴ So the LCM of the given numbers is 5 x 76 x 115 = 43700
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 5/43700
Therefore, the GCF of Fractions 355/380,420/575 is 5/43700
Least Common Multiple of 380,575 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 380,575 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(380,575) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(380,575) x common factors =5 x 1 = 5
LCM(380,575) = ( 380 × 575 ) / 5
LCM(380,575) = 218500 / 5
LCM(380,575) = 43700
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FAQs on GCF of Fractions of 355/380, 420/575
1. What is the HCF of 355,420?
The HCF of 355,420 is 5
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 355/380, 420/575?
Answer: GCF of Numerators as per given numbers 355/380, 420/575 is
GCF of Numerators i.e. for 355,420 is 5
LCM of denominators i.e. for 380,575 is 43700.
Thus, GCF of Fractions is 5/43700.Finally, GCF of Fractions for 355/380, 420/575 is 5/43700.