GCF of 36/75, 768/81, 294/148
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 36/75, 768/81, 294/148 i.e 6/299700 easily. The following is the detailed procedure to determine the greatest common factor of fractions 36/75, 768/81, 294/148.
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 36/75,768/81,294/148?
Given fractions are 36/75,768/81,294/148
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 36/75,768/81,294/148, numerators are 36,768,294
Denominators are 75,81,148
The GCF of 36,768,294 is 6 .
LCM of 75,81,148 is 299700.
The greatest common factor of 36/75,768/81,294/148 = [GCF of 36,768,294]/[LCM of 75,81,148]= 6/299700
Therefore, the GCF of 36/75,768/81,294/148 is 6/299700.
To find the highest common factor of 36,768,294, we have to find the factors of both numbers and list the highest common factor.
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36
The factors of 768 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 128, 192, 256, 384, 768
The factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294
The HCF of 36,768,294 is 6.
Lets's calculate GCF of 36,768,294
| 2 | 36, 768, 294 |
| 3 | 18, 384, 147 |
| 6, 128, 49 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 36,768,294 By Matching Biggest Common Factor Method
Now, list down the factors of 36
:1,2,3,4,6,9,12,18,36
Now, list down the factors of 768
:1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,256,384,768
Now, list down the factors of 294
:1,2,3,6,7,14,21,42,49,98,147,294
Greatest Common Factor
We found the factors 36,768,294 . The biggest common factor number is the GCF number.
So the greatest common factor 36,768,294 is 6.
Lets's calculate LCM of 75,81,148
| 3 | 75, 81, 148 |
| 25, 27, 148 |
∴ So the LCM of the given numbers is 3 x 25 x 27 x 148 = 299700
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/299700
Therefore, the GCF of Fractions 36/75,768/81,294/148 is 6/299700
Least Common Multiple of 75,81,148 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 75,81,148 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,81,148) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(75,81,148) x common factors =1 x 3 = 3
LCM(75,81,148) = ( 75 × 81 × 148 ) / 3
LCM(75,81,148) = 899100 / 3
LCM(75,81,148) = 299700
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 36/75, 768/81, 294/148
1. What is the HCF of 36,768,294?
The HCF of 36,768,294 is 6
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 36/75, 768/81, 294/148?
Answer: GCF of Numerators as per given numbers 36/75, 768/81, 294/148 is
GCF of Numerators i.e. for 36,768,294 is 6
LCM of denominators i.e. for 75,81,148 is 299700.
Thus, GCF of Fractions is 6/299700.Finally, GCF of Fractions for 36/75, 768/81, 294/148 is 6/299700.