GCF of 375/860, 314/415
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 375/860, 314/415 i.e 1/71380 easily. The following is the detailed procedure to determine the greatest common factor of fractions 375/860, 314/415.
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 375/860,314/415?
Given fractions are 375/860,314/415
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 375/860,314/415, numerators are 375,314
Denominators are 860,415
The GCF of 375,314 is 1 .
LCM of 860,415 is 71380.
The greatest common factor of 375/860,314/415 = [GCF of 375,314]/[LCM of 860,415]= 1/71380
Therefore, the GCF of 375/860,314/415 is 1/71380.
To find the highest common factor of 375,314, we have to find the factors of both numbers and list the highest common factor.
The factors of 375 are 1, 3, 5, 15, 25, 75, 125, 375
The factors of 314 are 1, 2, 157, 314
The HCF of 375,314 is 1.
Lets's calculate GCF of 375,314
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 375,314 By Matching Biggest Common Factor Method
Now, list down the factors of 375
:1,3,5,15,25,75,125,375
Now, list down the factors of 314
:1,2,157,314
Greatest Common Factor
We found the factors 375,314 . The biggest common factor number is the GCF number.
So the greatest common factor 375,314 is 1.
Lets's calculate LCM of 860,415
| 5 | 860, 415 |
| 172, 83 |
∴ So the LCM of the given numbers is 5 x 172 x 83 = 71380
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/71380
Therefore, the GCF of Fractions 375/860,314/415 is 1/71380
Least Common Multiple of 860,415 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 860,415 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(860,415) = 5
common factors(in case of two or more numbers have common factors) = 1
GCF(860,415) x common factors =5 x 1 = 5
LCM(860,415) = ( 860 × 415 ) / 5
LCM(860,415) = 356900 / 5
LCM(860,415) = 71380
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FAQs on GCF of Fractions of 375/860, 314/415
1. What is the HCF of 375,314?
The HCF of 375,314 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 375/860, 314/415?
Answer: GCF of Numerators as per given numbers 375/860, 314/415 is
GCF of Numerators i.e. for 375,314 is 1
LCM of denominators i.e. for 860,415 is 71380.
Thus, GCF of Fractions is 1/71380.Finally, GCF of Fractions for 375/860, 314/415 is 1/71380.