Use our free GCF of Fractions Calculator tool to compute the GCF of 42/74, 300/22, 616/519 i.e 2/422466 easily. The following is the detailed procedure to determine the greatest common factor of fractions 42/74, 300/22, 616/519.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 42/74,300/22,616/519
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 42/74,300/22,616/519, numerators are 42,300,616
Denominators are 74,22,519
The GCF of 42,300,616 is 2 .
LCM of 74,22,519 is 422466.
The greatest common factor of 42/74,300/22,616/519 = [GCF of 42,300,616]/[LCM of 74,22,519]= 2/422466
Therefore, the GCF of 42/74,300/22,616/519 is 2/422466.
To find the highest common factor of 42,300,616, we have to find the factors of both numbers and list the highest common factor.
The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42
The factors of 300 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 25, 30, 50, 60, 75, 100, 150, 300
The factors of 616 are 1, 2, 4, 7, 8, 11, 14, 22, 28, 44, 56, 77, 88, 154, 308, 616
The HCF of 42,300,616 is 2.
Lets's calculate GCF of 42,300,616
2 | 42, 300, 616 |
21, 150, 308 |
∴ So the GCF of the given numbers is 2 = 2
Now, list down the factors of 42
:1,2,3,6,7,14,21,42
Now, list down the factors of 300
:1,2,3,4,5,6,10,12,15,20,25,30,50,60,75,100,150,300
Now, list down the factors of 616
:1,2,4,7,8,11,14,22,28,44,56,77,88,154,308,616
Greatest Common Factor
We found the factors 42,300,616 . The biggest common factor number is the GCF number.
So the greatest common factor 42,300,616 is 2.
Lets's calculate LCM of 74,22,519
2 | 74, 22, 519 |
37, 11, 519 |
∴ So the LCM of the given numbers is 2 x 37 x 11 x 519 = 422466
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/422466
Therefore, the GCF of Fractions 42/74,300/22,616/519 is 2/422466
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 74,22,519 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(74,22,519) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(74,22,519) x common factors =1 x 2 = 2
LCM(74,22,519) = ( 74 × 22 × 519 ) / 2
LCM(74,22,519) = 844932 / 2
LCM(74,22,519) = 422466
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 42,300,616?
The HCF of 42,300,616 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 42/74, 300/22, 616/519?
Answer: GCF of Numerators as per given numbers 42/74, 300/22, 616/519 is
GCF of Numerators i.e. for 42,300,616 is 2
LCM of denominators i.e. for 74,22,519 is 422466.
Thus, GCF of Fractions is 2/422466.Finally, GCF of Fractions for 42/74, 300/22, 616/519 is 2/422466.