GCF of 84/515, 12/252, 804/840
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 84/515, 12/252, 804/840 i.e 12/259560 easily. The following is the detailed procedure to determine the greatest common factor of fractions 84/515, 12/252, 804/840.
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 84/515,12/252,804/840?
Given fractions are 84/515,12/252,804/840
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 84/515,12/252,804/840, numerators are 84,12,804
Denominators are 515,252,840
The GCF of 84,12,804 is 12 .
LCM of 515,252,840 is 259560.
The greatest common factor of 84/515,12/252,804/840 = [GCF of 84,12,804]/[LCM of 515,252,840]= 12/259560
Therefore, the GCF of 84/515,12/252,804/840 is 12/259560.
To find the highest common factor of 84,12,804, we have to find the factors of both numbers and list the highest common factor.
The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
The factors of 12 are 1, 2, 3, 4, 6, 12
The factors of 804 are 1, 2, 3, 4, 6, 12, 67, 134, 201, 268, 402, 804
The HCF of 84,12,804 is 12.
Lets's calculate GCF of 84,12,804
| 2 | 84, 12, 804 |
| 2 | 42, 6, 402 |
| 3 | 21, 3, 201 |
| 7, 1, 67 |
∴ So the GCF of the given numbers is 2 x 2 x 3 = 12
Greatest Common Factor of 84,12,804 By Matching Biggest Common Factor Method
Now, list down the factors of 84
:1,2,3,4,6,7,12,14,21,28,42,84
Now, list down the factors of 12
:1,2,3,4,6,12
Now, list down the factors of 804
:1,2,3,4,6,12,67,134,201,268,402,804
Greatest Common Factor
We found the factors 84,12,804 . The biggest common factor number is the GCF number.
So the greatest common factor 84,12,804 is 12.
Lets's calculate LCM of 515,252,840
| 2 | 515, 252, 840 |
| 2 | 515, 126, 420 |
| 3 | 515, 63, 210 |
| 5 | 515, 21, 70 |
| 7 | 103, 21, 14 |
| 103, 3, 2 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 5 x 7 x 103 x 3 x 2 = 259560
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 12/259560
Therefore, the GCF of Fractions 84/515,12/252,804/840 is 12/259560
Least Common Multiple of 515,252,840 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 515,252,840 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(515,252,840) = 1
common factors(in case of two or more numbers have common factors) = 420
GCF(515,252,840) x common factors =1 x 420 = 420
LCM(515,252,840) = ( 515 × 252 × 840 ) / 420
LCM(515,252,840) = 109015200 / 420
LCM(515,252,840) = 259560
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FAQs on GCF of Fractions of 84/515, 12/252, 804/840
1. What is the HCF of 84,12,804?
The HCF of 84,12,804 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 84/515, 12/252, 804/840?
Answer: GCF of Numerators as per given numbers 84/515, 12/252, 804/840 is
GCF of Numerators i.e. for 84,12,804 is 12
LCM of denominators i.e. for 515,252,840 is 259560.
Thus, GCF of Fractions is 12/259560.Finally, GCF of Fractions for 84/515, 12/252, 804/840 is 12/259560.