GCF of 774/289, 6072/969
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 774/289, 6072/969 i.e 6/16473 easily. The following is the detailed procedure to determine the greatest common factor of fractions 774/289, 6072/969.
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 774/289,6072/969?
Given fractions are 774/289,6072/969
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 774/289,6072/969, numerators are 774,6072
Denominators are 289,969
The GCF of 774,6072 is 6 .
LCM of 289,969 is 16473.
The greatest common factor of 774/289,6072/969 = [GCF of 774,6072]/[LCM of 289,969]= 6/16473
Therefore, the GCF of 774/289,6072/969 is 6/16473.
To find the highest common factor of 774,6072, we have to find the factors of both numbers and list the highest common factor.
The factors of 774 are 1, 2, 3, 6, 9, 18, 43, 86, 129, 258, 387, 774
The factors of 6072 are 1, 2, 3, 4, 6, 8, 11, 12, 22, 23, 24, 33, 44, 46, 66, 69, 88, 92, 132, 138, 184, 253, 264, 276, 506, 552, 759, 1012, 1518, 2024, 3036, 6072
The HCF of 774,6072 is 6.
Lets's calculate GCF of 774,6072
| 2 | 774, 6072 |
| 3 | 387, 3036 |
| 129, 1012 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 774,6072 By Matching Biggest Common Factor Method
Now, list down the factors of 774
:1,2,3,6,9,18,43,86,129,258,387,774
Now, list down the factors of 6072
:1,2,3,4,6,8,11,12,22,23,24,33,44,46,66,69,88,92,132,138,184,253,264,276,506,552,759,1012,1518,2024,3036,6072
Greatest Common Factor
We found the factors 774,6072 . The biggest common factor number is the GCF number.
So the greatest common factor 774,6072 is 6.
Lets's calculate LCM of 289,969
| 17 | 289, 969 |
| 17, 57 |
∴ So the LCM of the given numbers is 17 x 17 x 57 = 16473
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/16473
Therefore, the GCF of Fractions 774/289,6072/969 is 6/16473
Least Common Multiple of 289,969 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 289,969 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(289,969) = 17
common factors(in case of two or more numbers have common factors) = 1
GCF(289,969) x common factors =17 x 1 = 17
LCM(289,969) = ( 289 × 969 ) / 17
LCM(289,969) = 280041 / 17
LCM(289,969) = 16473
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FAQs on GCF of Fractions of 774/289, 6072/969
1. What is the HCF of 774,6072?
The HCF of 774,6072 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 774/289, 6072/969?
Answer: GCF of Numerators as per given numbers 774/289, 6072/969 is
GCF of Numerators i.e. for 774,6072 is 6
LCM of denominators i.e. for 289,969 is 16473.
Thus, GCF of Fractions is 6/16473.Finally, GCF of Fractions for 774/289, 6072/969 is 6/16473.