GCF of 666/13, 684/253
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 666/13, 684/253 i.e 18/3289 easily. The following is the detailed procedure to determine the greatest common factor of fractions 666/13, 684/253.
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 666/13,684/253?
Given fractions are 666/13,684/253
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 666/13,684/253, numerators are 666,684
Denominators are 13,253
The GCF of 666,684 is 18 .
LCM of 13,253 is 3289.
The greatest common factor of 666/13,684/253 = [GCF of 666,684]/[LCM of 13,253]= 18/3289
Therefore, the GCF of 666/13,684/253 is 18/3289.
To find the highest common factor of 666,684, we have to find the factors of both numbers and list the highest common factor.
The factors of 666 are 1, 2, 3, 6, 9, 18, 37, 74, 111, 222, 333, 666
The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The HCF of 666,684 is 18.
Lets's calculate GCF of 666,684
| 2 | 666, 684 |
| 3 | 333, 342 |
| 3 | 111, 114 |
| 37, 38 |
∴ So the GCF of the given numbers is 2 x 3 x 3 = 18
Greatest Common Factor of 666,684 By Matching Biggest Common Factor Method
Now, list down the factors of 666
:1,2,3,6,9,18,37,74,111,222,333,666
Now, list down the factors of 684
:1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Greatest Common Factor
We found the factors 666,684 . The biggest common factor number is the GCF number.
So the greatest common factor 666,684 is 18.
Lets's calculate LCM of 13,253
Given numbers has no common factors except 1. So, there LCM is their product i.e 3289
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 18/3289
Therefore, the GCF of Fractions 666/13,684/253 is 18/3289
Least Common Multiple of 13,253 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 13,253 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(13,253) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(13,253) x common factors =1 x 1 = 1
LCM(13,253) = ( 13 × 253 ) / 1
LCM(13,253) = 3289 / 1
LCM(13,253) = 3289
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FAQs on GCF of Fractions of 666/13, 684/253
1. What is the HCF of 666,684?
The HCF of 666,684 is 18
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 666/13, 684/253?
Answer: GCF of Numerators as per given numbers 666/13, 684/253 is
GCF of Numerators i.e. for 666,684 is 18
LCM of denominators i.e. for 13,253 is 3289.
Thus, GCF of Fractions is 18/3289.Finally, GCF of Fractions for 666/13, 684/253 is 18/3289.