GCF of 2952/208, 1729/308
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2952/208, 1729/308 i.e 1/16016 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2952/208, 1729/308.
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 2952/208,1729/308?
Given fractions are 2952/208,1729/308
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 2952/208,1729/308, numerators are 2952,1729
Denominators are 208,308
The GCF of 2952,1729 is 1 .
LCM of 208,308 is 16016.
The greatest common factor of 2952/208,1729/308 = [GCF of 2952,1729]/[LCM of 208,308]= 1/16016
Therefore, the GCF of 2952/208,1729/308 is 1/16016.
To find the highest common factor of 2952,1729, we have to find the factors of both numbers and list the highest common factor.
The factors of 2952 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 41, 72, 82, 123, 164, 246, 328, 369, 492, 738, 984, 1476, 2952
The factors of 1729 are 1, 7, 13, 19, 91, 133, 247, 1729
The HCF of 2952,1729 is 1.
Lets's calculate GCF of 2952,1729
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 2952,1729 By Matching Biggest Common Factor Method
Now, list down the factors of 2952
:1,2,3,4,6,8,9,12,18,24,36,41,72,82,123,164,246,328,369,492,738,984,1476,2952
Now, list down the factors of 1729
:1,7,13,19,91,133,247,1729
Greatest Common Factor
We found the factors 2952,1729 . The biggest common factor number is the GCF number.
So the greatest common factor 2952,1729 is 1.
Lets's calculate LCM of 208,308
| 2 | 208, 308 |
| 2 | 104, 154 |
| 52, 77 |
∴ So the LCM of the given numbers is 2 x 2 x 52 x 77 = 16016
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/16016
Therefore, the GCF of Fractions 2952/208,1729/308 is 1/16016
Least Common Multiple of 208,308 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 208,308 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(208,308) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(208,308) x common factors =4 x 1 = 4
LCM(208,308) = ( 208 × 308 ) / 4
LCM(208,308) = 64064 / 4
LCM(208,308) = 16016
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FAQs on GCF of Fractions of 2952/208, 1729/308
1. What is the HCF of 2952,1729?
The HCF of 2952,1729 is 1
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 2952/208, 1729/308?
Answer: GCF of Numerators as per given numbers 2952/208, 1729/308 is
GCF of Numerators i.e. for 2952,1729 is 1
LCM of denominators i.e. for 208,308 is 16016.
Thus, GCF of Fractions is 1/16016.Finally, GCF of Fractions for 2952/208, 1729/308 is 1/16016.