GCF of 3214/869, 3138/523
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3214/869, 3138/523 i.e 2/454487 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3214/869, 3138/523.
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 3214/869,3138/523?
Given fractions are 3214/869,3138/523
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 3214/869,3138/523, numerators are 3214,3138
Denominators are 869,523
The GCF of 3214,3138 is 2 .
LCM of 869,523 is 454487.
The greatest common factor of 3214/869,3138/523 = [GCF of 3214,3138]/[LCM of 869,523]= 2/454487
Therefore, the GCF of 3214/869,3138/523 is 2/454487.
To find the highest common factor of 3214,3138, we have to find the factors of both numbers and list the highest common factor.
The factors of 3214 are 1, 2, 1607, 3214
The factors of 3138 are 1, 2, 3, 6, 523, 1046, 1569, 3138
The HCF of 3214,3138 is 2.
Lets's calculate GCF of 3214,3138
| 2 | 3214, 3138 |
| 1607, 1569 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 3214,3138 By Matching Biggest Common Factor Method
Now, list down the factors of 3214
:1,2,1607,3214
Now, list down the factors of 3138
:1,2,3,6,523,1046,1569,3138
Greatest Common Factor
We found the factors 3214,3138 . The biggest common factor number is the GCF number.
So the greatest common factor 3214,3138 is 2.
Lets's calculate LCM of 869,523
Given numbers has no common factors except 1. So, there LCM is their product i.e 454487
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/454487
Therefore, the GCF of Fractions 3214/869,3138/523 is 2/454487
Least Common Multiple of 869,523 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 869,523 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(869,523) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(869,523) x common factors =1 x 1 = 1
LCM(869,523) = ( 869 × 523 ) / 1
LCM(869,523) = 454487 / 1
LCM(869,523) = 454487
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FAQs on GCF of Fractions of 3214/869, 3138/523
1. What is the HCF of 3214,3138?
The HCF of 3214,3138 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 3214/869, 3138/523?
Answer: GCF of Numerators as per given numbers 3214/869, 3138/523 is
GCF of Numerators i.e. for 3214,3138 is 2
LCM of denominators i.e. for 869,523 is 454487.
Thus, GCF of Fractions is 2/454487.Finally, GCF of Fractions for 3214/869, 3138/523 is 2/454487.