GCF of 349/28, 412/49, 361/61
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 349/28, 412/49, 361/61 i.e 1/11956 easily. The following is the detailed procedure to determine the greatest common factor of fractions 349/28, 412/49, 361/61.
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 349/28,412/49,361/61?
Given fractions are 349/28,412/49,361/61
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 349/28,412/49,361/61, numerators are 349,412,361
Denominators are 28,49,61
The GCF of 349,412,361 is 1 .
LCM of 28,49,61 is 11956.
The greatest common factor of 349/28,412/49,361/61 = [GCF of 349,412,361]/[LCM of 28,49,61]= 1/11956
Therefore, the GCF of 349/28,412/49,361/61 is 1/11956.
To find the highest common factor of 349,412,361, we have to find the factors of both numbers and list the highest common factor.
The factors of 349 are 1, 349
The factors of 412 are 1, 2, 4, 103, 206, 412
The factors of 361 are 1, 19, 361
The HCF of 349,412,361 is 1.
Lets's calculate GCF of 349,412,361
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 349,412,361 By Matching Biggest Common Factor Method
Now, list down the factors of 349
:1,349
Now, list down the factors of 412
:1,2,4,103,206,412
Now, list down the factors of 361
:1,19,361
Greatest Common Factor
We found the factors 349,412,361 . The biggest common factor number is the GCF number.
So the greatest common factor 349,412,361 is 1.
Lets's calculate LCM of 28,49,61
| 7 | 28, 49, 61 |
| 4, 7, 61 |
∴ So the LCM of the given numbers is 7 x 4 x 7 x 61 = 11956
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/11956
Therefore, the GCF of Fractions 349/28,412/49,361/61 is 1/11956
Least Common Multiple of 28,49,61 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 28,49,61 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(28,49,61) = 1
common factors(in case of two or more numbers have common factors) = 7
GCF(28,49,61) x common factors =1 x 7 = 7
LCM(28,49,61) = ( 28 × 49 × 61 ) / 7
LCM(28,49,61) = 83692 / 7
LCM(28,49,61) = 11956
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FAQs on GCF of Fractions of 349/28, 412/49, 361/61
1. What is the HCF of 349,412,361?
The HCF of 349,412,361 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 349/28, 412/49, 361/61?
Answer: GCF of Numerators as per given numbers 349/28, 412/49, 361/61 is
GCF of Numerators i.e. for 349,412,361 is 1
LCM of denominators i.e. for 28,49,61 is 11956.
Thus, GCF of Fractions is 1/11956.Finally, GCF of Fractions for 349/28, 412/49, 361/61 is 1/11956.