GCF of 2305/310, 1682/1427
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2305/310, 1682/1427 i.e 1/442370 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2305/310, 1682/1427.
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 2305/310,1682/1427?
Given fractions are 2305/310,1682/1427
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 2305/310,1682/1427, numerators are 2305,1682
Denominators are 310,1427
The GCF of 2305,1682 is 1 .
LCM of 310,1427 is 442370.
The greatest common factor of 2305/310,1682/1427 = [GCF of 2305,1682]/[LCM of 310,1427]= 1/442370
Therefore, the GCF of 2305/310,1682/1427 is 1/442370.
To find the highest common factor of 2305,1682, we have to find the factors of both numbers and list the highest common factor.
The factors of 2305 are 1, 5, 461, 2305
The factors of 1682 are 1, 2, 29, 58, 841, 1682
The HCF of 2305,1682 is 1.
Lets's calculate GCF of 2305,1682
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 2305,1682 By Matching Biggest Common Factor Method
Now, list down the factors of 2305
:1,5,461,2305
Now, list down the factors of 1682
:1,2,29,58,841,1682
Greatest Common Factor
We found the factors 2305,1682 . The biggest common factor number is the GCF number.
So the greatest common factor 2305,1682 is 1.
Lets's calculate LCM of 310,1427
Given numbers has no common factors except 1. So, there LCM is their product i.e 442370
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/442370
Therefore, the GCF of Fractions 2305/310,1682/1427 is 1/442370
Least Common Multiple of 310,1427 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 310,1427 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(310,1427) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(310,1427) x common factors =1 x 1 = 1
LCM(310,1427) = ( 310 × 1427 ) / 1
LCM(310,1427) = 442370 / 1
LCM(310,1427) = 442370
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FAQs on GCF of Fractions of 2305/310, 1682/1427
1. What is the HCF of 2305,1682?
The HCF of 2305,1682 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 2305/310, 1682/1427?
Answer: GCF of Numerators as per given numbers 2305/310, 1682/1427 is
GCF of Numerators i.e. for 2305,1682 is 1
LCM of denominators i.e. for 310,1427 is 442370.
Thus, GCF of Fractions is 1/442370.Finally, GCF of Fractions for 2305/310, 1682/1427 is 1/442370.