GCF of 292/14, 280/49, 660/13
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 292/14, 280/49, 660/13 i.e 4/1274 easily. The following is the detailed procedure to determine the greatest common factor of fractions 292/14, 280/49, 660/13.
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 292/14,280/49,660/13?
Given fractions are 292/14,280/49,660/13
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 292/14,280/49,660/13, numerators are 292,280,660
Denominators are 14,49,13
The GCF of 292,280,660 is 4 .
LCM of 14,49,13 is 1274.
The greatest common factor of 292/14,280/49,660/13 = [GCF of 292,280,660]/[LCM of 14,49,13]= 4/1274
Therefore, the GCF of 292/14,280/49,660/13 is 4/1274.
To find the highest common factor of 292,280,660, we have to find the factors of both numbers and list the highest common factor.
The factors of 292 are 1, 2, 4, 73, 146, 292
The factors of 280 are 1, 2, 4, 5, 7, 8, 10, 14, 20, 28, 35, 40, 56, 70, 140, 280
The factors of 660 are 1, 2, 3, 4, 5, 6, 10, 11, 12, 15, 20, 22, 30, 33, 44, 55, 60, 66, 110, 132, 165, 220, 330, 660
The HCF of 292,280,660 is 4.
Lets's calculate GCF of 292,280,660
| 2 | 292, 280, 660 |
| 2 | 146, 140, 330 |
| 73, 70, 165 |
∴ So the GCF of the given numbers is 2 x 2 = 4
Greatest Common Factor of 292,280,660 By Matching Biggest Common Factor Method
Now, list down the factors of 292
:1,2,4,73,146,292
Now, list down the factors of 280
:1,2,4,5,7,8,10,14,20,28,35,40,56,70,140,280
Now, list down the factors of 660
:1,2,3,4,5,6,10,11,12,15,20,22,30,33,44,55,60,66,110,132,165,220,330,660
Greatest Common Factor
We found the factors 292,280,660 . The biggest common factor number is the GCF number.
So the greatest common factor 292,280,660 is 4.
Lets's calculate LCM of 14,49,13
| 7 | 14, 49, 13 |
| 2, 7, 13 |
∴ So the LCM of the given numbers is 7 x 2 x 7 x 13 = 1274
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 4/1274
Therefore, the GCF of Fractions 292/14,280/49,660/13 is 4/1274
Least Common Multiple of 14,49,13 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 14,49,13 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(14,49,13) = 1
common factors(in case of two or more numbers have common factors) = 7
GCF(14,49,13) x common factors =1 x 7 = 7
LCM(14,49,13) = ( 14 × 49 × 13 ) / 7
LCM(14,49,13) = 8918 / 7
LCM(14,49,13) = 1274
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FAQs on GCF of Fractions of 292/14, 280/49, 660/13
1. What is the HCF of 292,280,660?
The HCF of 292,280,660 is 4
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 292/14, 280/49, 660/13?
Answer: GCF of Numerators as per given numbers 292/14, 280/49, 660/13 is
GCF of Numerators i.e. for 292,280,660 is 4
LCM of denominators i.e. for 14,49,13 is 1274.
Thus, GCF of Fractions is 4/1274.Finally, GCF of Fractions for 292/14, 280/49, 660/13 is 4/1274.