GCF of 664/33, 656/678
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 664/33, 656/678 i.e 8/7458 easily. The following is the detailed procedure to determine the greatest common factor of fractions 664/33, 656/678.
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 664/33,656/678?
Given fractions are 664/33,656/678
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 664/33,656/678, numerators are 664,656
Denominators are 33,678
The GCF of 664,656 is 8 .
LCM of 33,678 is 7458.
The greatest common factor of 664/33,656/678 = [GCF of 664,656]/[LCM of 33,678]= 8/7458
Therefore, the GCF of 664/33,656/678 is 8/7458.
To find the highest common factor of 664,656, we have to find the factors of both numbers and list the highest common factor.
The factors of 664 are 1, 2, 4, 8, 83, 166, 332, 664
The factors of 656 are 1, 2, 4, 8, 16, 41, 82, 164, 328, 656
The HCF of 664,656 is 8.
Lets's calculate GCF of 664,656
| 2 | 664, 656 |
| 2 | 332, 328 |
| 2 | 166, 164 |
| 83, 82 |
∴ So the GCF of the given numbers is 2 x 2 x 2 = 8
Greatest Common Factor of 664,656 By Matching Biggest Common Factor Method
Now, list down the factors of 664
:1,2,4,8,83,166,332,664
Now, list down the factors of 656
:1,2,4,8,16,41,82,164,328,656
Greatest Common Factor
We found the factors 664,656 . The biggest common factor number is the GCF number.
So the greatest common factor 664,656 is 8.
Lets's calculate LCM of 33,678
| 3 | 33, 678 |
| 11, 226 |
∴ So the LCM of the given numbers is 3 x 11 x 226 = 7458
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 8/7458
Therefore, the GCF of Fractions 664/33,656/678 is 8/7458
Least Common Multiple of 33,678 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 33,678 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(33,678) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(33,678) x common factors =3 x 1 = 3
LCM(33,678) = ( 33 × 678 ) / 3
LCM(33,678) = 22374 / 3
LCM(33,678) = 7458
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FAQs on GCF of Fractions of 664/33, 656/678
1. What is the HCF of 664,656?
The HCF of 664,656 is 8
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 664/33, 656/678?
Answer: GCF of Numerators as per given numbers 664/33, 656/678 is
GCF of Numerators i.e. for 664,656 is 8
LCM of denominators i.e. for 33,678 is 7458.
Thus, GCF of Fractions is 8/7458.Finally, GCF of Fractions for 664/33, 656/678 is 8/7458.