GCF of 759/75, 271/78, 985/35
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 759/75, 271/78, 985/35 i.e 1/13650 easily. The following is the detailed procedure to determine the greatest common factor of fractions 759/75, 271/78, 985/35.
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 759/75,271/78,985/35?
Given fractions are 759/75,271/78,985/35
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 759/75,271/78,985/35, numerators are 759,271,985
Denominators are 75,78,35
The GCF of 759,271,985 is 1 .
LCM of 75,78,35 is 13650.
The greatest common factor of 759/75,271/78,985/35 = [GCF of 759,271,985]/[LCM of 75,78,35]= 1/13650
Therefore, the GCF of 759/75,271/78,985/35 is 1/13650.
To find the highest common factor of 759,271,985, we have to find the factors of both numbers and list the highest common factor.
The factors of 759 are 1, 3, 11, 23, 33, 69, 253, 759
The factors of 271 are 1, 271
The factors of 985 are 1, 5, 197, 985
The HCF of 759,271,985 is 1.
Lets's calculate GCF of 759,271,985
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 759,271,985 By Matching Biggest Common Factor Method
Now, list down the factors of 759
:1,3,11,23,33,69,253,759
Now, list down the factors of 271
:1,271
Now, list down the factors of 985
:1,5,197,985
Greatest Common Factor
We found the factors 759,271,985 . The biggest common factor number is the GCF number.
So the greatest common factor 759,271,985 is 1.
Lets's calculate LCM of 75,78,35
| 3 | 75, 78, 35 |
| 5 | 25, 26, 35 |
| 5, 26, 7 |
∴ So the LCM of the given numbers is 3 x 5 x 5 x 26 x 7 = 13650
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/13650
Therefore, the GCF of Fractions 759/75,271/78,985/35 is 1/13650
Least Common Multiple of 75,78,35 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 75,78,35 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(75,78,35) = 1
common factors(in case of two or more numbers have common factors) = 15
GCF(75,78,35) x common factors =1 x 15 = 15
LCM(75,78,35) = ( 75 × 78 × 35 ) / 15
LCM(75,78,35) = 204750 / 15
LCM(75,78,35) = 13650
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FAQs on GCF of Fractions of 759/75, 271/78, 985/35
1. What is the HCF of 759,271,985?
The HCF of 759,271,985 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 759/75, 271/78, 985/35?
Answer: GCF of Numerators as per given numbers 759/75, 271/78, 985/35 is
GCF of Numerators i.e. for 759,271,985 is 1
LCM of denominators i.e. for 75,78,35 is 13650.
Thus, GCF of Fractions is 1/13650.Finally, GCF of Fractions for 759/75, 271/78, 985/35 is 1/13650.