GCF of 6976/272, 2122/656
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6976/272, 2122/656 i.e 2/11152 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6976/272, 2122/656.
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 6976/272,2122/656?
Given fractions are 6976/272,2122/656
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 6976/272,2122/656, numerators are 6976,2122
Denominators are 272,656
The GCF of 6976,2122 is 2 .
LCM of 272,656 is 11152.
The greatest common factor of 6976/272,2122/656 = [GCF of 6976,2122]/[LCM of 272,656]= 2/11152
Therefore, the GCF of 6976/272,2122/656 is 2/11152.
To find the highest common factor of 6976,2122, we have to find the factors of both numbers and list the highest common factor.
The factors of 6976 are 1, 2, 4, 8, 16, 32, 64, 109, 218, 436, 872, 1744, 3488, 6976
The factors of 2122 are 1, 2, 1061, 2122
The HCF of 6976,2122 is 2.
Lets's calculate GCF of 6976,2122
| 2 | 6976, 2122 |
| 3488, 1061 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 6976,2122 By Matching Biggest Common Factor Method
Now, list down the factors of 6976
:1,2,4,8,16,32,64,109,218,436,872,1744,3488,6976
Now, list down the factors of 2122
:1,2,1061,2122
Greatest Common Factor
We found the factors 6976,2122 . The biggest common factor number is the GCF number.
So the greatest common factor 6976,2122 is 2.
Lets's calculate LCM of 272,656
| 2 | 272, 656 |
| 2 | 136, 328 |
| 2 | 68, 164 |
| 2 | 34, 82 |
| 17, 41 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 17 x 41 = 11152
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/11152
Therefore, the GCF of Fractions 6976/272,2122/656 is 2/11152
Least Common Multiple of 272,656 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 272,656 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(272,656) = 16
common factors(in case of two or more numbers have common factors) = 1
GCF(272,656) x common factors =16 x 1 = 16
LCM(272,656) = ( 272 × 656 ) / 16
LCM(272,656) = 178432 / 16
LCM(272,656) = 11152
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FAQs on GCF of Fractions of 6976/272, 2122/656
1. What is the HCF of 6976,2122?
The HCF of 6976,2122 is 2
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 6976/272, 2122/656?
Answer: GCF of Numerators as per given numbers 6976/272, 2122/656 is
GCF of Numerators i.e. for 6976,2122 is 2
LCM of denominators i.e. for 272,656 is 11152.
Thus, GCF of Fractions is 2/11152.Finally, GCF of Fractions for 6976/272, 2122/656 is 2/11152.