GCF of 156/305, 134/119, 212/387
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 156/305, 134/119, 212/387 i.e 2/14046165 easily. The following is the detailed procedure to determine the greatest common factor of fractions 156/305, 134/119, 212/387.
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 156/305,134/119,212/387?
Given fractions are 156/305,134/119,212/387
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 156/305,134/119,212/387, numerators are 156,134,212
Denominators are 305,119,387
The GCF of 156,134,212 is 2 .
LCM of 305,119,387 is 14046165.
The greatest common factor of 156/305,134/119,212/387 = [GCF of 156,134,212]/[LCM of 305,119,387]= 2/14046165
Therefore, the GCF of 156/305,134/119,212/387 is 2/14046165.
To find the highest common factor of 156,134,212, we have to find the factors of both numbers and list the highest common factor.
The factors of 156 are 1, 2, 3, 4, 6, 12, 13, 26, 39, 52, 78, 156
The factors of 134 are 1, 2, 67, 134
The factors of 212 are 1, 2, 4, 53, 106, 212
The HCF of 156,134,212 is 2.
Lets's calculate GCF of 156,134,212
| 2 | 156, 134, 212 |
| 78, 67, 106 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 156,134,212 By Matching Biggest Common Factor Method
Now, list down the factors of 156
:1,2,3,4,6,12,13,26,39,52,78,156
Now, list down the factors of 134
:1,2,67,134
Now, list down the factors of 212
:1,2,4,53,106,212
Greatest Common Factor
We found the factors 156,134,212 . The biggest common factor number is the GCF number.
So the greatest common factor 156,134,212 is 2.
Lets's calculate LCM of 305,119,387
Given numbers has no common factors except 1. So, there LCM is their product i.e 14046165
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/14046165
Therefore, the GCF of Fractions 156/305,134/119,212/387 is 2/14046165
Least Common Multiple of 305,119,387 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 305,119,387 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(305,119,387) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(305,119,387) x common factors =1 x 1 = 1
LCM(305,119,387) = ( 305 × 119 × 387 ) / 1
LCM(305,119,387) = 14046165 / 1
LCM(305,119,387) = 14046165
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FAQs on GCF of Fractions of 156/305, 134/119, 212/387
1. What is the HCF of 156,134,212?
The HCF of 156,134,212 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 156/305, 134/119, 212/387?
Answer: GCF of Numerators as per given numbers 156/305, 134/119, 212/387 is
GCF of Numerators i.e. for 156,134,212 is 2
LCM of denominators i.e. for 305,119,387 is 14046165.
Thus, GCF of Fractions is 2/14046165.Finally, GCF of Fractions for 156/305, 134/119, 212/387 is 2/14046165.