GCF of 663/32, 680/664
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 663/32, 680/664 i.e 17/2656 easily. The following is the detailed procedure to determine the greatest common factor of fractions 663/32, 680/664.
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 663/32,680/664?
Given fractions are 663/32,680/664
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 663/32,680/664, numerators are 663,680
Denominators are 32,664
The GCF of 663,680 is 17 .
LCM of 32,664 is 2656.
The greatest common factor of 663/32,680/664 = [GCF of 663,680]/[LCM of 32,664]= 17/2656
Therefore, the GCF of 663/32,680/664 is 17/2656.
To find the highest common factor of 663,680, we have to find the factors of both numbers and list the highest common factor.
The factors of 663 are 1, 3, 13, 17, 39, 51, 221, 663
The factors of 680 are 1, 2, 4, 5, 8, 10, 17, 20, 34, 40, 68, 85, 136, 170, 340, 680
The HCF of 663,680 is 17.
Lets's calculate GCF of 663,680
| 17 | 663, 680 |
| 39, 40 |
∴ So the GCF of the given numbers is 17 = 17
Greatest Common Factor of 663,680 By Matching Biggest Common Factor Method
Now, list down the factors of 663
:1,3,13,17,39,51,221,663
Now, list down the factors of 680
:1,2,4,5,8,10,17,20,34,40,68,85,136,170,340,680
Greatest Common Factor
We found the factors 663,680 . The biggest common factor number is the GCF number.
So the greatest common factor 663,680 is 17.
Lets's calculate LCM of 32,664
| 2 | 32, 664 |
| 2 | 16, 332 |
| 2 | 8, 166 |
| 4, 83 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 4 x 83 = 2656
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 17/2656
Therefore, the GCF of Fractions 663/32,680/664 is 17/2656
Least Common Multiple of 32,664 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 32,664 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,664) = 8
common factors(in case of two or more numbers have common factors) = 1
GCF(32,664) x common factors =8 x 1 = 8
LCM(32,664) = ( 32 × 664 ) / 8
LCM(32,664) = 21248 / 8
LCM(32,664) = 2656
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FAQs on GCF of Fractions of 663/32, 680/664
1. What is the HCF of 663,680?
The HCF of 663,680 is 17
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 663/32, 680/664?
Answer: GCF of Numerators as per given numbers 663/32, 680/664 is
GCF of Numerators i.e. for 663,680 is 17
LCM of denominators i.e. for 32,664 is 2656.
Thus, GCF of Fractions is 17/2656.Finally, GCF of Fractions for 663/32, 680/664 is 17/2656.