GCF of 2970/728, 8742/350
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 2970/728, 8742/350 i.e 6/18200 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2970/728, 8742/350.
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 2970/728,8742/350?
Given fractions are 2970/728,8742/350
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 2970/728,8742/350, numerators are 2970,8742
Denominators are 728,350
The GCF of 2970,8742 is 6 .
LCM of 728,350 is 18200.
The greatest common factor of 2970/728,8742/350 = [GCF of 2970,8742]/[LCM of 728,350]= 6/18200
Therefore, the GCF of 2970/728,8742/350 is 6/18200.
To find the highest common factor of 2970,8742, we have to find the factors of both numbers and list the highest common factor.
The factors of 2970 are 1, 2, 3, 5, 6, 9, 10, 11, 15, 18, 22, 27, 30, 33, 45, 54, 55, 66, 90, 99, 110, 135, 165, 198, 270, 297, 330, 495, 594, 990, 1485, 2970
The factors of 8742 are 1, 2, 3, 6, 31, 47, 62, 93, 94, 141, 186, 282, 1457, 2914, 4371, 8742
The HCF of 2970,8742 is 6.
Lets's calculate GCF of 2970,8742
| 2 | 2970, 8742 |
| 3 | 1485, 4371 |
| 495, 1457 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 2970,8742 By Matching Biggest Common Factor Method
Now, list down the factors of 2970
:1,2,3,5,6,9,10,11,15,18,22,27,30,33,45,54,55,66,90,99,110,135,165,198,270,297,330,495,594,990,1485,2970
Now, list down the factors of 8742
:1,2,3,6,31,47,62,93,94,141,186,282,1457,2914,4371,8742
Greatest Common Factor
We found the factors 2970,8742 . The biggest common factor number is the GCF number.
So the greatest common factor 2970,8742 is 6.
Lets's calculate LCM of 728,350
| 2 | 728, 350 |
| 7 | 364, 175 |
| 52, 25 |
∴ So the LCM of the given numbers is 2 x 7 x 52 x 25 = 18200
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/18200
Therefore, the GCF of Fractions 2970/728,8742/350 is 6/18200
Least Common Multiple of 728,350 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 728,350 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(728,350) = 14
common factors(in case of two or more numbers have common factors) = 1
GCF(728,350) x common factors =14 x 1 = 14
LCM(728,350) = ( 728 × 350 ) / 14
LCM(728,350) = 254800 / 14
LCM(728,350) = 18200
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FAQs on GCF of Fractions of 2970/728, 8742/350
1. What is the HCF of 2970,8742?
The HCF of 2970,8742 is 6
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 2970/728, 8742/350?
Answer: GCF of Numerators as per given numbers 2970/728, 8742/350 is
GCF of Numerators i.e. for 2970,8742 is 6
LCM of denominators i.e. for 728,350 is 18200.
Thus, GCF of Fractions is 6/18200.Finally, GCF of Fractions for 2970/728, 8742/350 is 6/18200.