GCF of 5738/384, 1465/8174
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 5738/384, 1465/8174 i.e 1/1569408 easily. The following is the detailed procedure to determine the greatest common factor of fractions 5738/384, 1465/8174.
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 5738/384,1465/8174?
Given fractions are 5738/384,1465/8174
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 5738/384,1465/8174, numerators are 5738,1465
Denominators are 384,8174
The GCF of 5738,1465 is 1 .
LCM of 384,8174 is 1569408.
The greatest common factor of 5738/384,1465/8174 = [GCF of 5738,1465]/[LCM of 384,8174]= 1/1569408
Therefore, the GCF of 5738/384,1465/8174 is 1/1569408.
To find the highest common factor of 5738,1465, we have to find the factors of both numbers and list the highest common factor.
The factors of 5738 are 1, 2, 19, 38, 151, 302, 2869, 5738
The factors of 1465 are 1, 5, 293, 1465
The HCF of 5738,1465 is 1.
Lets's calculate GCF of 5738,1465
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 5738,1465 By Matching Biggest Common Factor Method
Now, list down the factors of 5738
:1,2,19,38,151,302,2869,5738
Now, list down the factors of 1465
:1,5,293,1465
Greatest Common Factor
We found the factors 5738,1465 . The biggest common factor number is the GCF number.
So the greatest common factor 5738,1465 is 1.
Lets's calculate LCM of 384,8174
| 2 | 384, 8174 |
| 192, 4087 |
∴ So the LCM of the given numbers is 2 x 192 x 4087 = 1569408
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1569408
Therefore, the GCF of Fractions 5738/384,1465/8174 is 1/1569408
Least Common Multiple of 384,8174 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 384,8174 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(384,8174) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(384,8174) x common factors =2 x 1 = 2
LCM(384,8174) = ( 384 × 8174 ) / 2
LCM(384,8174) = 3138816 / 2
LCM(384,8174) = 1569408
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FAQs on GCF of Fractions of 5738/384, 1465/8174
1. What is the HCF of 5738,1465?
The HCF of 5738,1465 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 5738/384, 1465/8174?
Answer: GCF of Numerators as per given numbers 5738/384, 1465/8174 is
GCF of Numerators i.e. for 5738,1465 is 1
LCM of denominators i.e. for 384,8174 is 1569408.
Thus, GCF of Fractions is 1/1569408.Finally, GCF of Fractions for 5738/384, 1465/8174 is 1/1569408.