GCF of 812/64, 462/43, 149/31
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 812/64, 462/43, 149/31 i.e 1/85312 easily. The following is the detailed procedure to determine the greatest common factor of fractions 812/64, 462/43, 149/31.
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 812/64,462/43,149/31?
Given fractions are 812/64,462/43,149/31
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 812/64,462/43,149/31, numerators are 812,462,149
Denominators are 64,43,31
The GCF of 812,462,149 is 1 .
LCM of 64,43,31 is 85312.
The greatest common factor of 812/64,462/43,149/31 = [GCF of 812,462,149]/[LCM of 64,43,31]= 1/85312
Therefore, the GCF of 812/64,462/43,149/31 is 1/85312.
To find the highest common factor of 812,462,149, we have to find the factors of both numbers and list the highest common factor.
The factors of 812 are 1, 2, 4, 7, 14, 28, 29, 58, 116, 203, 406, 812
The factors of 462 are 1, 2, 3, 6, 7, 11, 14, 21, 22, 33, 42, 66, 77, 154, 231, 462
The factors of 149 are 1, 149
The HCF of 812,462,149 is 1.
Lets's calculate GCF of 812,462,149
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 812,462,149 By Matching Biggest Common Factor Method
Now, list down the factors of 812
:1,2,4,7,14,28,29,58,116,203,406,812
Now, list down the factors of 462
:1,2,3,6,7,11,14,21,22,33,42,66,77,154,231,462
Now, list down the factors of 149
:1,149
Greatest Common Factor
We found the factors 812,462,149 . The biggest common factor number is the GCF number.
So the greatest common factor 812,462,149 is 1.
Lets's calculate LCM of 64,43,31
Given numbers has no common factors except 1. So, there LCM is their product i.e 85312
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/85312
Therefore, the GCF of Fractions 812/64,462/43,149/31 is 1/85312
Least Common Multiple of 64,43,31 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 64,43,31 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(64,43,31) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(64,43,31) x common factors =1 x 1 = 1
LCM(64,43,31) = ( 64 × 43 × 31 ) / 1
LCM(64,43,31) = 85312 / 1
LCM(64,43,31) = 85312
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FAQs on GCF of Fractions of 812/64, 462/43, 149/31
1. What is the HCF of 812,462,149?
The HCF of 812,462,149 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 812/64, 462/43, 149/31?
Answer: GCF of Numerators as per given numbers 812/64, 462/43, 149/31 is
GCF of Numerators i.e. for 812,462,149 is 1
LCM of denominators i.e. for 64,43,31 is 85312.
Thus, GCF of Fractions is 1/85312.Finally, GCF of Fractions for 812/64, 462/43, 149/31 is 1/85312.