GCF of 155/512, 748/814
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 155/512, 748/814 i.e 1/208384 easily. The following is the detailed procedure to determine the greatest common factor of fractions 155/512, 748/814.
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 155/512,748/814?
Given fractions are 155/512,748/814
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 155/512,748/814, numerators are 155,748
Denominators are 512,814
The GCF of 155,748 is 1 .
LCM of 512,814 is 208384.
The greatest common factor of 155/512,748/814 = [GCF of 155,748]/[LCM of 512,814]= 1/208384
Therefore, the GCF of 155/512,748/814 is 1/208384.
To find the highest common factor of 155,748, we have to find the factors of both numbers and list the highest common factor.
The factors of 155 are 1, 5, 31, 155
The factors of 748 are 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748
The HCF of 155,748 is 1.
Lets's calculate GCF of 155,748
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 155,748 By Matching Biggest Common Factor Method
Now, list down the factors of 155
:1,5,31,155
Now, list down the factors of 748
:1,2,4,11,17,22,34,44,68,187,374,748
Greatest Common Factor
We found the factors 155,748 . The biggest common factor number is the GCF number.
So the greatest common factor 155,748 is 1.
Lets's calculate LCM of 512,814
| 2 | 512, 814 |
| 256, 407 |
∴ So the LCM of the given numbers is 2 x 256 x 407 = 208384
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/208384
Therefore, the GCF of Fractions 155/512,748/814 is 1/208384
Least Common Multiple of 512,814 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 512,814 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(512,814) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(512,814) x common factors =2 x 1 = 2
LCM(512,814) = ( 512 × 814 ) / 2
LCM(512,814) = 416768 / 2
LCM(512,814) = 208384
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FAQs on GCF of Fractions of 155/512, 748/814
1. What is the HCF of 155,748?
The HCF of 155,748 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 155/512, 748/814?
Answer: GCF of Numerators as per given numbers 155/512, 748/814 is
GCF of Numerators i.e. for 155,748 is 1
LCM of denominators i.e. for 512,814 is 208384.
Thus, GCF of Fractions is 1/208384.Finally, GCF of Fractions for 155/512, 748/814 is 1/208384.