GCF of 665/10, 217/734
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 665/10, 217/734 i.e 7/3670 easily. The following is the detailed procedure to determine the greatest common factor of fractions 665/10, 217/734.
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 665/10,217/734?
Given fractions are 665/10,217/734
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 665/10,217/734, numerators are 665,217
Denominators are 10,734
The GCF of 665,217 is 7 .
LCM of 10,734 is 3670.
The greatest common factor of 665/10,217/734 = [GCF of 665,217]/[LCM of 10,734]= 7/3670
Therefore, the GCF of 665/10,217/734 is 7/3670.
To find the highest common factor of 665,217, we have to find the factors of both numbers and list the highest common factor.
The factors of 665 are 1, 5, 7, 19, 35, 95, 133, 665
The factors of 217 are 1, 7, 31, 217
The HCF of 665,217 is 7.
Lets's calculate GCF of 665,217
| 7 | 665, 217 |
| 95, 31 |
∴ So the GCF of the given numbers is 7 = 7
Greatest Common Factor of 665,217 By Matching Biggest Common Factor Method
Now, list down the factors of 665
:1,5,7,19,35,95,133,665
Now, list down the factors of 217
:1,7,31,217
Greatest Common Factor
We found the factors 665,217 . The biggest common factor number is the GCF number.
So the greatest common factor 665,217 is 7.
Lets's calculate LCM of 10,734
| 2 | 10, 734 |
| 5, 367 |
∴ So the LCM of the given numbers is 2 x 5 x 367 = 3670
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 7/3670
Therefore, the GCF of Fractions 665/10,217/734 is 7/3670
Least Common Multiple of 10,734 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 10,734 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(10,734) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(10,734) x common factors =2 x 1 = 2
LCM(10,734) = ( 10 × 734 ) / 2
LCM(10,734) = 7340 / 2
LCM(10,734) = 3670
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FAQs on GCF of Fractions of 665/10, 217/734
1. What is the HCF of 665,217?
The HCF of 665,217 is 7
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 665/10, 217/734?
Answer: GCF of Numerators as per given numbers 665/10, 217/734 is
GCF of Numerators i.e. for 665,217 is 7
LCM of denominators i.e. for 10,734 is 3670.
Thus, GCF of Fractions is 7/3670.Finally, GCF of Fractions for 665/10, 217/734 is 7/3670.