GCF of 675/713, 729/170
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 675/713, 729/170 i.e 27/121210 easily. The following is the detailed procedure to determine the greatest common factor of fractions 675/713, 729/170.
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 675/713,729/170?
Given fractions are 675/713,729/170
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 675/713,729/170, numerators are 675,729
Denominators are 713,170
The GCF of 675,729 is 27 .
LCM of 713,170 is 121210.
The greatest common factor of 675/713,729/170 = [GCF of 675,729]/[LCM of 713,170]= 27/121210
Therefore, the GCF of 675/713,729/170 is 27/121210.
To find the highest common factor of 675,729, we have to find the factors of both numbers and list the highest common factor.
The factors of 675 are 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, 675
The factors of 729 are 1, 3, 9, 27, 81, 243, 729
The HCF of 675,729 is 27.
Lets's calculate GCF of 675,729
| 3 | 675, 729 |
| 3 | 225, 243 |
| 3 | 75, 81 |
| 25, 27 |
∴ So the GCF of the given numbers is 3 x 3 x 3 = 27
Greatest Common Factor of 675,729 By Matching Biggest Common Factor Method
Now, list down the factors of 675
:1,3,5,9,15,25,27,45,75,135,225,675
Now, list down the factors of 729
:1,3,9,27,81,243,729
Greatest Common Factor
We found the factors 675,729 . The biggest common factor number is the GCF number.
So the greatest common factor 675,729 is 27.
Lets's calculate LCM of 713,170
Given numbers has no common factors except 1. So, there LCM is their product i.e 121210
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 27/121210
Therefore, the GCF of Fractions 675/713,729/170 is 27/121210
Least Common Multiple of 713,170 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 713,170 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(713,170) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(713,170) x common factors =1 x 1 = 1
LCM(713,170) = ( 713 × 170 ) / 1
LCM(713,170) = 121210 / 1
LCM(713,170) = 121210
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FAQs on GCF of Fractions of 675/713, 729/170
1. What is the HCF of 675,729?
The HCF of 675,729 is 27
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 675/713, 729/170?
Answer: GCF of Numerators as per given numbers 675/713, 729/170 is
GCF of Numerators i.e. for 675,729 is 27
LCM of denominators i.e. for 713,170 is 121210.
Thus, GCF of Fractions is 27/121210.Finally, GCF of Fractions for 675/713, 729/170 is 27/121210.