Use our free GCF of Fractions Calculator tool to compute the GCF of 72/17, 132/74, 784/608 i.e 4/382432 easily. The following is the detailed procedure to determine the greatest common factor of fractions 72/17, 132/74, 784/608.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
Given fractions are 72/17,132/74,784/608
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 72/17,132/74,784/608, numerators are 72,132,784
Denominators are 17,74,608
The GCF of 72,132,784 is 4 .
LCM of 17,74,608 is 382432.
The greatest common factor of 72/17,132/74,784/608 = [GCF of 72,132,784]/[LCM of 17,74,608]= 4/382432
Therefore, the GCF of 72/17,132/74,784/608 is 4/382432.
To find the highest common factor of 72,132,784, we have to find the factors of both numbers and list the highest common factor.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
The factors of 132 are 1, 2, 3, 4, 6, 11, 12, 22, 33, 44, 66, 132
The factors of 784 are 1, 2, 4, 7, 8, 14, 16, 28, 49, 56, 98, 112, 196, 392, 784
The HCF of 72,132,784 is 4.
Lets's calculate GCF of 72,132,784
2 | 72, 132, 784 |
2 | 36, 66, 392 |
18, 33, 196 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Now, list down the factors of 72
:1,2,3,4,6,8,9,12,18,24,36,72
Now, list down the factors of 132
:1,2,3,4,6,11,12,22,33,44,66,132
Now, list down the factors of 784
:1,2,4,7,8,14,16,28,49,56,98,112,196,392,784
Greatest Common Factor
We found the factors 72,132,784 . The biggest common factor number is the GCF number.
So the greatest common factor 72,132,784 is 4.
Lets's calculate LCM of 17,74,608
2 | 17, 74, 608 |
17, 37, 304 |
∴ So the LCM of the given numbers is 2 x 17 x 37 x 304 = 382432
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/382432
Therefore, the GCF of Fractions 72/17,132/74,784/608 is 4/382432
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 17,74,608 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(17,74,608) = 1
common factors(in case of two or more numbers have common factors) = 2
GCF(17,74,608) x common factors =1 x 2 = 2
LCM(17,74,608) = ( 17 × 74 × 608 ) / 2
LCM(17,74,608) = 764864 / 2
LCM(17,74,608) = 382432
Here are some samples of GCF of Fractions calculations.
1. What is the HCF of 72,132,784?
The HCF of 72,132,784 is 4
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 72/17, 132/74, 784/608?
Answer: GCF of Numerators as per given numbers 72/17, 132/74, 784/608 is
GCF of Numerators i.e. for 72,132,784 is 4
LCM of denominators i.e. for 17,74,608 is 382432.
Thus, GCF of Fractions is 4/382432.Finally, GCF of Fractions for 72/17, 132/74, 784/608 is 4/382432.