GCF of 3420/648, 9132/867
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 3420/648, 9132/867 i.e 12/187272 easily. The following is the detailed procedure to determine the greatest common factor of fractions 3420/648, 9132/867.
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 3420/648,9132/867?
Given fractions are 3420/648,9132/867
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 3420/648,9132/867, numerators are 3420,9132
Denominators are 648,867
The GCF of 3420,9132 is 12 .
LCM of 648,867 is 187272.
The greatest common factor of 3420/648,9132/867 = [GCF of 3420,9132]/[LCM of 648,867]= 12/187272
Therefore, the GCF of 3420/648,9132/867 is 12/187272.
To find the highest common factor of 3420,9132, we have to find the factors of both numbers and list the highest common factor.
The factors of 3420 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 19, 20, 30, 36, 38, 45, 57, 60, 76, 90, 95, 114, 171, 180, 190, 228, 285, 342, 380, 570, 684, 855, 1140, 1710, 3420
The factors of 9132 are 1, 2, 3, 4, 6, 12, 761, 1522, 2283, 3044, 4566, 9132
The HCF of 3420,9132 is 12.
Lets's calculate GCF of 3420,9132
| 2 | 3420, 9132 |
| 2 | 1710, 4566 |
| 3 | 855, 2283 |
| 285, 761 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 3420,9132 By Matching Biggest Common Factor Method
Now, list down the factors of 3420
:1,2,3,4,5,6,9,10,12,15,18,19,20,30,36,38,45,57,60,76,90,95,114,171,180,190,228,285,342,380,570,684,855,1140,1710,3420
Now, list down the factors of 9132
:1,2,3,4,6,12,761,1522,2283,3044,4566,9132
Greatest Common Factor
We found the factors 3420,9132 . The biggest common factor number is the GCF number.
So the greatest common factor 3420,9132 is 12.
Lets's calculate LCM of 648,867
| 3 | 648, 867 |
| 216, 289 |
∴ So the LCM of the given numbers is 3 x 216 x 289 = 187272
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/187272
Therefore, the GCF of Fractions 3420/648,9132/867 is 12/187272
Least Common Multiple of 648,867 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 648,867 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(648,867) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(648,867) x common factors =3 x 1 = 3
LCM(648,867) = ( 648 × 867 ) / 3
LCM(648,867) = 561816 / 3
LCM(648,867) = 187272
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FAQs on GCF of Fractions of 3420/648, 9132/867
1. What is the HCF of 3420,9132?
The HCF of 3420,9132 is 12
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 3420/648, 9132/867?
Answer: GCF of Numerators as per given numbers 3420/648, 9132/867 is
GCF of Numerators i.e. for 3420,9132 is 12
LCM of denominators i.e. for 648,867 is 187272.
Thus, GCF of Fractions is 12/187272.Finally, GCF of Fractions for 3420/648, 9132/867 is 12/187272.