GCF of 328/21, 310/74, 442/14
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 328/21, 310/74, 442/14 i.e 2/1554 easily. The following is the detailed procedure to determine the greatest common factor of fractions 328/21, 310/74, 442/14.
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 328/21,310/74,442/14?
Given fractions are 328/21,310/74,442/14
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 328/21,310/74,442/14, numerators are 328,310,442
Denominators are 21,74,14
The GCF of 328,310,442 is 2 .
LCM of 21,74,14 is 1554.
The greatest common factor of 328/21,310/74,442/14 = [GCF of 328,310,442]/[LCM of 21,74,14]= 2/1554
Therefore, the GCF of 328/21,310/74,442/14 is 2/1554.
To find the highest common factor of 328,310,442, we have to find the factors of both numbers and list the highest common factor.
The factors of 328 are 1, 2, 4, 8, 41, 82, 164, 328
The factors of 310 are 1, 2, 5, 10, 31, 62, 155, 310
The factors of 442 are 1, 2, 13, 17, 26, 34, 221, 442
The HCF of 328,310,442 is 2.
Lets's calculate GCF of 328,310,442
| 2 | 328, 310, 442 |
| 164, 155, 221 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 328,310,442 By Matching Biggest Common Factor Method
Now, list down the factors of 328
:1,2,4,8,41,82,164,328
Now, list down the factors of 310
:1,2,5,10,31,62,155,310
Now, list down the factors of 442
:1,2,13,17,26,34,221,442
Greatest Common Factor
We found the factors 328,310,442 . The biggest common factor number is the GCF number.
So the greatest common factor 328,310,442 is 2.
Lets's calculate LCM of 21,74,14
| 2 | 21, 74, 14 |
| 7 | 21, 37, 7 |
| 3, 37, 1 |
∴ So the LCM of the given numbers is 2 x 7 x 3 x 37 x 1 = 1554
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/1554
Therefore, the GCF of Fractions 328/21,310/74,442/14 is 2/1554
Least Common Multiple of 21,74,14 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 21,74,14 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,74,14) = 1
common factors(in case of two or more numbers have common factors) = 14
GCF(21,74,14) x common factors =1 x 14 = 14
LCM(21,74,14) = ( 21 × 74 × 14 ) / 14
LCM(21,74,14) = 21756 / 14
LCM(21,74,14) = 1554
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FAQs on GCF of Fractions of 328/21, 310/74, 442/14
1. What is the HCF of 328,310,442?
The HCF of 328,310,442 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 328/21, 310/74, 442/14?
Answer: GCF of Numerators as per given numbers 328/21, 310/74, 442/14 is
GCF of Numerators i.e. for 328,310,442 is 2
LCM of denominators i.e. for 21,74,14 is 1554.
Thus, GCF of Fractions is 2/1554.Finally, GCF of Fractions for 328/21, 310/74, 442/14 is 2/1554.