GCF of 852/409, 375/421
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 852/409, 375/421 i.e 3/172189 easily. The following is the detailed procedure to determine the greatest common factor of fractions 852/409, 375/421.
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 852/409,375/421?
Given fractions are 852/409,375/421
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 852/409,375/421, numerators are 852,375
Denominators are 409,421
The GCF of 852,375 is 3 .
LCM of 409,421 is 172189.
The greatest common factor of 852/409,375/421 = [GCF of 852,375]/[LCM of 409,421]= 3/172189
Therefore, the GCF of 852/409,375/421 is 3/172189.
To find the highest common factor of 852,375, we have to find the factors of both numbers and list the highest common factor.
The factors of 852 are 1, 2, 3, 4, 6, 12, 71, 142, 213, 284, 426, 852
The factors of 375 are 1, 3, 5, 15, 25, 75, 125, 375
The HCF of 852,375 is 3.
Lets's calculate GCF of 852,375
| 3 | 852, 375 |
| 284, 125 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 852,375 By Matching Biggest Common Factor Method
Now, list down the factors of 852
:1,2,3,4,6,12,71,142,213,284,426,852
Now, list down the factors of 375
:1,3,5,15,25,75,125,375
Greatest Common Factor
We found the factors 852,375 . The biggest common factor number is the GCF number.
So the greatest common factor 852,375 is 3.
Lets's calculate LCM of 409,421
Given numbers has no common factors except 1. So, there LCM is their product i.e 172189
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/172189
Therefore, the GCF of Fractions 852/409,375/421 is 3/172189
Least Common Multiple of 409,421 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 409,421 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(409,421) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(409,421) x common factors =1 x 1 = 1
LCM(409,421) = ( 409 × 421 ) / 1
LCM(409,421) = 172189 / 1
LCM(409,421) = 172189
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FAQs on GCF of Fractions of 852/409, 375/421
1. What is the HCF of 852,375?
The HCF of 852,375 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 852/409, 375/421?
Answer: GCF of Numerators as per given numbers 852/409, 375/421 is
GCF of Numerators i.e. for 852,375 is 3
LCM of denominators i.e. for 409,421 is 172189.
Thus, GCF of Fractions is 3/172189.Finally, GCF of Fractions for 852/409, 375/421 is 3/172189.