Use our free GCF of Fractions Calculator tool to compute the GCF of 342/862, 380/144 i.e 38/62064 easily. The following is the detailed procedure to determine the greatest common factor of fractions 342/862, 380/144.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 342/862,380/144
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 342/862,380/144, numerators are 342,380
Denominators are 862,144
The GCF of 342,380 is 38 .
LCM of 862,144 is 62064.
The greatest common factor of 342/862,380/144 = [GCF of 342,380]/[LCM of 862,144]= 38/62064
Therefore, the GCF of 342/862,380/144 is 38/62064.
To find the highest common factor of 342,380, we have to find the factors of both numbers and list the highest common factor.
The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
The factors of 380 are 1, 2, 4, 5, 10, 19, 20, 38, 76, 95, 190, 380
The HCF of 342,380 is 38.
Lets's calculate GCF of 342,380
2 | 342, 380 |
19 | 171, 190 |
9, 10 |
∴ So the GCF of the given numbers is 2 x 19 = 38
Now, list down the factors of 342
:1,2,3,6,9,18,19,38,57,114,171,342
Now, list down the factors of 380
:1,2,4,5,10,19,20,38,76,95,190,380
Greatest Common Factor
We found the factors 342,380 . The biggest common factor number is the GCF number.
So the greatest common factor 342,380 is 38.
Lets's calculate LCM of 862,144
2 | 862, 144 |
431, 72 |
∴ So the LCM of the given numbers is 2 x 431 x 72 = 62064
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 38/62064
Therefore, the GCF of Fractions 342/862,380/144 is 38/62064
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 862,144 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(862,144) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(862,144) x common factors =2 x 1 = 2
LCM(862,144) = ( 862 × 144 ) / 2
LCM(862,144) = 124128 / 2
LCM(862,144) = 62064
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 342,380?
The HCF of 342,380 is 38
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 342/862, 380/144?
Answer: GCF of Numerators as per given numbers 342/862, 380/144 is
GCF of Numerators i.e. for 342,380 is 38
LCM of denominators i.e. for 862,144 is 62064.
Thus, GCF of Fractions is 38/62064.Finally, GCF of Fractions for 342/862, 380/144 is 38/62064.