GCF of 508/101, 814/102
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 508/101, 814/102 i.e 2/10302 easily. The following is the detailed procedure to determine the greatest common factor of fractions 508/101, 814/102.
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 508/101,814/102?
Given fractions are 508/101,814/102
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 508/101,814/102, numerators are 508,814
Denominators are 101,102
The GCF of 508,814 is 2 .
LCM of 101,102 is 10302.
The greatest common factor of 508/101,814/102 = [GCF of 508,814]/[LCM of 101,102]= 2/10302
Therefore, the GCF of 508/101,814/102 is 2/10302.
To find the highest common factor of 508,814, we have to find the factors of both numbers and list the highest common factor.
The factors of 508 are 1, 2, 4, 127, 254, 508
The factors of 814 are 1, 2, 11, 22, 37, 74, 407, 814
The HCF of 508,814 is 2.
Lets's calculate GCF of 508,814
| 2 | 508, 814 |
| 254, 407 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 508,814 By Matching Biggest Common Factor Method
Now, list down the factors of 508
:1,2,4,127,254,508
Now, list down the factors of 814
:1,2,11,22,37,74,407,814
Greatest Common Factor
We found the factors 508,814 . The biggest common factor number is the GCF number.
So the greatest common factor 508,814 is 2.
Lets's calculate LCM of 101,102
Given numbers has no common factors except 1. So, there LCM is their product i.e 10302
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/10302
Therefore, the GCF of Fractions 508/101,814/102 is 2/10302
Least Common Multiple of 101,102 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 101,102 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(101,102) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(101,102) x common factors =1 x 1 = 1
LCM(101,102) = ( 101 × 102 ) / 1
LCM(101,102) = 10302 / 1
LCM(101,102) = 10302
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FAQs on GCF of Fractions of 508/101, 814/102
1. What is the HCF of 508,814?
The HCF of 508,814 is 2
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 508/101, 814/102?
Answer: GCF of Numerators as per given numbers 508/101, 814/102 is
GCF of Numerators i.e. for 508,814 is 2
LCM of denominators i.e. for 101,102 is 10302.
Thus, GCF of Fractions is 2/10302.Finally, GCF of Fractions for 508/101, 814/102 is 2/10302.