GCF of 21/342, 38/114, 440/155
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 21/342, 38/114, 440/155 i.e 1/53010 easily. The following is the detailed procedure to determine the greatest common factor of fractions 21/342, 38/114, 440/155.
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 21/342,38/114,440/155?
Given fractions are 21/342,38/114,440/155
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 21/342,38/114,440/155, numerators are 21,38,440
Denominators are 342,114,155
The GCF of 21,38,440 is 1 .
LCM of 342,114,155 is 53010.
The greatest common factor of 21/342,38/114,440/155 = [GCF of 21,38,440]/[LCM of 342,114,155]= 1/53010
Therefore, the GCF of 21/342,38/114,440/155 is 1/53010.
To find the highest common factor of 21,38,440, we have to find the factors of both numbers and list the highest common factor.
The factors of 21 are 1, 3, 7, 21
The factors of 38 are 1, 2, 19, 38
The factors of 440 are 1, 2, 4, 5, 8, 10, 11, 20, 22, 40, 44, 55, 88, 110, 220, 440
The HCF of 21,38,440 is 1.
Lets's calculate GCF of 21,38,440
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 21,38,440 By Matching Biggest Common Factor Method
Now, list down the factors of 21
:1,3,7,21
Now, list down the factors of 38
:1,2,19,38
Now, list down the factors of 440
:1,2,4,5,8,10,11,20,22,40,44,55,88,110,220,440
Greatest Common Factor
We found the factors 21,38,440 . The biggest common factor number is the GCF number.
So the greatest common factor 21,38,440 is 1.
Lets's calculate LCM of 342,114,155
| 2 | 342, 114, 155 |
| 3 | 171, 57, 155 |
| 19 | 19, 57, 155 |
| 1, 3, 155 |
∴ So the LCM of the given numbers is 2 x 3 x 19 x 1 x 3 x 155 = 53010
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/53010
Therefore, the GCF of Fractions 21/342,38/114,440/155 is 1/53010
Least Common Multiple of 342,114,155 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 342,114,155 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(342,114,155) = 1
common factors(in case of two or more numbers have common factors) = 114
GCF(342,114,155) x common factors =1 x 114 = 114
LCM(342,114,155) = ( 342 × 114 × 155 ) / 114
LCM(342,114,155) = 6043140 / 114
LCM(342,114,155) = 53010
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FAQs on GCF of Fractions of 21/342, 38/114, 440/155
1. What is the HCF of 21,38,440?
The HCF of 21,38,440 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 21/342, 38/114, 440/155?
Answer: GCF of Numerators as per given numbers 21/342, 38/114, 440/155 is
GCF of Numerators i.e. for 21,38,440 is 1
LCM of denominators i.e. for 342,114,155 is 53010.
Thus, GCF of Fractions is 1/53010.Finally, GCF of Fractions for 21/342, 38/114, 440/155 is 1/53010.