GCF of 97/390, 75/396, 342/728
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 97/390, 75/396, 342/728 i.e 1/360360 easily. The following is the detailed procedure to determine the greatest common factor of fractions 97/390, 75/396, 342/728.
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 97/390,75/396,342/728?
Given fractions are 97/390,75/396,342/728
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 97/390,75/396,342/728, numerators are 97,75,342
Denominators are 390,396,728
The GCF of 97,75,342 is 1 .
LCM of 390,396,728 is 360360.
The greatest common factor of 97/390,75/396,342/728 = [GCF of 97,75,342]/[LCM of 390,396,728]= 1/360360
Therefore, the GCF of 97/390,75/396,342/728 is 1/360360.
To find the highest common factor of 97,75,342, we have to find the factors of both numbers and list the highest common factor.
The factors of 97 are 1, 97
The factors of 75 are 1, 3, 5, 15, 25, 75
The factors of 342 are 1, 2, 3, 6, 9, 18, 19, 38, 57, 114, 171, 342
The HCF of 97,75,342 is 1.
Lets's calculate GCF of 97,75,342
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 97,75,342 By Matching Biggest Common Factor Method
Now, list down the factors of 97
:1,97
Now, list down the factors of 75
:1,3,5,15,25,75
Now, list down the factors of 342
:1,2,3,6,9,18,19,38,57,114,171,342
Greatest Common Factor
We found the factors 97,75,342 . The biggest common factor number is the GCF number.
So the greatest common factor 97,75,342 is 1.
Lets's calculate LCM of 390,396,728
| 2 | 390, 396, 728 |
| 2 | 195, 198, 364 |
| 3 | 195, 99, 182 |
| 13 | 65, 33, 182 |
| 5, 33, 14 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 13 x 5 x 33 x 14 = 360360
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/360360
Therefore, the GCF of Fractions 97/390,75/396,342/728 is 1/360360
Least Common Multiple of 390,396,728 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 390,396,728 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(390,396,728) = 2
common factors(in case of two or more numbers have common factors) = 156
GCF(390,396,728) x common factors =2 x 156 = 312
LCM(390,396,728) = ( 390 × 396 × 728 ) / 312
LCM(390,396,728) = 112432320 / 312
LCM(390,396,728) = 360360
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FAQs on GCF of Fractions of 97/390, 75/396, 342/728
1. What is the HCF of 97,75,342?
The HCF of 97,75,342 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 97/390, 75/396, 342/728?
Answer: GCF of Numerators as per given numbers 97/390, 75/396, 342/728 is
GCF of Numerators i.e. for 97,75,342 is 1
LCM of denominators i.e. for 390,396,728 is 360360.
Thus, GCF of Fractions is 1/360360.Finally, GCF of Fractions for 97/390, 75/396, 342/728 is 1/360360.