GCF of 80/14, 412/49, 351/196
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 80/14, 412/49, 351/196 i.e 1/196 easily. The following is the detailed procedure to determine the greatest common factor of fractions 80/14, 412/49, 351/196.
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 80/14,412/49,351/196?
Given fractions are 80/14,412/49,351/196
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 80/14,412/49,351/196, numerators are 80,412,351
Denominators are 14,49,196
The GCF of 80,412,351 is 1 .
LCM of 14,49,196 is 196.
The greatest common factor of 80/14,412/49,351/196 = [GCF of 80,412,351]/[LCM of 14,49,196]= 1/196
Therefore, the GCF of 80/14,412/49,351/196 is 1/196.
To find the highest common factor of 80,412,351, we have to find the factors of both numbers and list the highest common factor.
The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80
The factors of 412 are 1, 2, 4, 103, 206, 412
The factors of 351 are 1, 3, 9, 13, 27, 39, 117, 351
The HCF of 80,412,351 is 1.
Lets's calculate GCF of 80,412,351
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 80,412,351 By Matching Biggest Common Factor Method
Now, list down the factors of 80
:1,2,4,5,8,10,16,20,40,80
Now, list down the factors of 412
:1,2,4,103,206,412
Now, list down the factors of 351
:1,3,9,13,27,39,117,351
Greatest Common Factor
We found the factors 80,412,351 . The biggest common factor number is the GCF number.
So the greatest common factor 80,412,351 is 1.
Lets's calculate LCM of 14,49,196
| 2 | 14, 49, 196 |
| 7 | 7, 49, 98 |
| 7 | 1, 7, 14 |
| 1, 1, 2 |
∴ So the LCM of the given numbers is 2 x 7 x 7 x 1 x 1 x 2 = 196
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/196
Therefore, the GCF of Fractions 80/14,412/49,351/196 is 1/196
Least Common Multiple of 14,49,196 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 14,49,196 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,49,196) = 7
common factors(in case of two or more numbers have common factors) = 98
GCF(14,49,196) x common factors =7 x 98 = 686
LCM(14,49,196) = ( 14 × 49 × 196 ) / 686
LCM(14,49,196) = 134456 / 686
LCM(14,49,196) = 196
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FAQs on GCF of Fractions of 80/14, 412/49, 351/196
1. What is the HCF of 80,412,351?
The HCF of 80,412,351 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 80/14, 412/49, 351/196?
Answer: GCF of Numerators as per given numbers 80/14, 412/49, 351/196 is
GCF of Numerators i.e. for 80,412,351 is 1
LCM of denominators i.e. for 14,49,196 is 196.
Thus, GCF of Fractions is 1/196.Finally, GCF of Fractions for 80/14, 412/49, 351/196 is 1/196.