GCF of 17/39, 706/35, 378/505
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 17/39, 706/35, 378/505 i.e 1/137865 easily. The following is the detailed procedure to determine the greatest common factor of fractions 17/39, 706/35, 378/505.
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 17/39,706/35,378/505?
Given fractions are 17/39,706/35,378/505
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 17/39,706/35,378/505, numerators are 17,706,378
Denominators are 39,35,505
The GCF of 17,706,378 is 1 .
LCM of 39,35,505 is 137865.
The greatest common factor of 17/39,706/35,378/505 = [GCF of 17,706,378]/[LCM of 39,35,505]= 1/137865
Therefore, the GCF of 17/39,706/35,378/505 is 1/137865.
To find the highest common factor of 17,706,378, we have to find the factors of both numbers and list the highest common factor.
The factors of 17 are 1, 17
The factors of 706 are 1, 2, 353, 706
The factors of 378 are 1, 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, 189, 378
The HCF of 17,706,378 is 1.
Lets's calculate GCF of 17,706,378
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 17,706,378 By Matching Biggest Common Factor Method
Now, list down the factors of 17
:1,17
Now, list down the factors of 706
:1,2,353,706
Now, list down the factors of 378
:1,2,3,6,7,9,14,18,21,27,42,54,63,126,189,378
Greatest Common Factor
We found the factors 17,706,378 . The biggest common factor number is the GCF number.
So the greatest common factor 17,706,378 is 1.
Lets's calculate LCM of 39,35,505
| 5 | 39, 35, 505 |
| 39, 7, 101 |
∴ So the LCM of the given numbers is 5 x 39 x 7 x 101 = 137865
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/137865
Therefore, the GCF of Fractions 17/39,706/35,378/505 is 1/137865
Least Common Multiple of 39,35,505 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 39,35,505 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(39,35,505) = 1
common factors(in case of two or more numbers have common factors) = 5
GCF(39,35,505) x common factors =1 x 5 = 5
LCM(39,35,505) = ( 39 × 35 × 505 ) / 5
LCM(39,35,505) = 689325 / 5
LCM(39,35,505) = 137865
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FAQs on GCF of Fractions of 17/39, 706/35, 378/505
1. What is the HCF of 17,706,378?
The HCF of 17,706,378 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 17/39, 706/35, 378/505?
Answer: GCF of Numerators as per given numbers 17/39, 706/35, 378/505 is
GCF of Numerators i.e. for 17,706,378 is 1
LCM of denominators i.e. for 39,35,505 is 137865.
Thus, GCF of Fractions is 1/137865.Finally, GCF of Fractions for 17/39, 706/35, 378/505 is 1/137865.