GCF of 311/56, 357/74, 133/21
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 311/56, 357/74, 133/21 i.e 1/6216 easily. The following is the detailed procedure to determine the greatest common factor of fractions 311/56, 357/74, 133/21.
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 311/56,357/74,133/21?
Given fractions are 311/56,357/74,133/21
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 311/56,357/74,133/21, numerators are 311,357,133
Denominators are 56,74,21
The GCF of 311,357,133 is 1 .
LCM of 56,74,21 is 6216.
The greatest common factor of 311/56,357/74,133/21 = [GCF of 311,357,133]/[LCM of 56,74,21]= 1/6216
Therefore, the GCF of 311/56,357/74,133/21 is 1/6216.
To find the highest common factor of 311,357,133, we have to find the factors of both numbers and list the highest common factor.
The factors of 311 are 1, 311
The factors of 357 are 1, 3, 7, 17, 21, 51, 119, 357
The factors of 133 are 1, 7, 19, 133
The HCF of 311,357,133 is 1.
Lets's calculate GCF of 311,357,133
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 311,357,133 By Matching Biggest Common Factor Method
Now, list down the factors of 311
:1,311
Now, list down the factors of 357
:1,3,7,17,21,51,119,357
Now, list down the factors of 133
:1,7,19,133
Greatest Common Factor
We found the factors 311,357,133 . The biggest common factor number is the GCF number.
So the greatest common factor 311,357,133 is 1.
Lets's calculate LCM of 56,74,21
| 2 | 56, 74, 21 |
| 7 | 28, 37, 21 |
| 4, 37, 3 |
∴ So the LCM of the given numbers is 2 x 7 x 4 x 37 x 3 = 6216
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/6216
Therefore, the GCF of Fractions 311/56,357/74,133/21 is 1/6216
Least Common Multiple of 56,74,21 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 56,74,21 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(56,74,21) = 1
common factors(in case of two or more numbers have common factors) = 14
GCF(56,74,21) x common factors =1 x 14 = 14
LCM(56,74,21) = ( 56 × 74 × 21 ) / 14
LCM(56,74,21) = 87024 / 14
LCM(56,74,21) = 6216
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FAQs on GCF of Fractions of 311/56, 357/74, 133/21
1. What is the HCF of 311,357,133?
The HCF of 311,357,133 is 1
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 311/56, 357/74, 133/21?
Answer: GCF of Numerators as per given numbers 311/56, 357/74, 133/21 is
GCF of Numerators i.e. for 311,357,133 is 1
LCM of denominators i.e. for 56,74,21 is 6216.
Thus, GCF of Fractions is 1/6216.Finally, GCF of Fractions for 311/56, 357/74, 133/21 is 1/6216.