GCF of 6864/148, 7689/6080
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 6864/148, 7689/6080 i.e 33/224960 easily. The following is the detailed procedure to determine the greatest common factor of fractions 6864/148, 7689/6080.
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 6864/148,7689/6080?
Given fractions are 6864/148,7689/6080
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 6864/148,7689/6080, numerators are 6864,7689
Denominators are 148,6080
The GCF of 6864,7689 is 33 .
LCM of 148,6080 is 224960.
The greatest common factor of 6864/148,7689/6080 = [GCF of 6864,7689]/[LCM of 148,6080]= 33/224960
Therefore, the GCF of 6864/148,7689/6080 is 33/224960.
To find the highest common factor of 6864,7689, we have to find the factors of both numbers and list the highest common factor.
The factors of 6864 are 1, 2, 3, 4, 6, 8, 11, 12, 13, 16, 22, 24, 26, 33, 39, 44, 48, 52, 66, 78, 88, 104, 132, 143, 156, 176, 208, 264, 286, 312, 429, 528, 572, 624, 858, 1144, 1716, 2288, 3432, 6864
The factors of 7689 are 1, 3, 11, 33, 233, 699, 2563, 7689
The HCF of 6864,7689 is 33.
Lets's calculate GCF of 6864,7689
| 3 | 6864, 7689 |
| 11 | 2288, 2563 |
| 208, 233 |
∴ So the GCF of the given numbers is 3 x 11 = 33
Greatest Common Factor of 6864,7689 By Matching Biggest Common Factor Method
Now, list down the factors of 6864
:1,2,3,4,6,8,11,12,13,16,22,24,26,33,39,44,48,52,66,78,88,104,132,143,156,176,208,264,286,312,429,528,572,624,858,1144,1716,2288,3432,6864
Now, list down the factors of 7689
:1,3,11,33,233,699,2563,7689
Greatest Common Factor
We found the factors 6864,7689 . The biggest common factor number is the GCF number.
So the greatest common factor 6864,7689 is 33.
Lets's calculate LCM of 148,6080
| 2 | 148, 6080 |
| 2 | 74, 3040 |
| 37, 1520 |
∴ So the LCM of the given numbers is 2 x 2 x 37 x 1520 = 224960
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 33/224960
Therefore, the GCF of Fractions 6864/148,7689/6080 is 33/224960
Least Common Multiple of 148,6080 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 148,6080 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(148,6080) = 4
common factors(in case of two or more numbers have common factors) = 1
GCF(148,6080) x common factors =4 x 1 = 4
LCM(148,6080) = ( 148 × 6080 ) / 4
LCM(148,6080) = 899840 / 4
LCM(148,6080) = 224960
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FAQs on GCF of Fractions of 6864/148, 7689/6080
1. What is the HCF of 6864,7689?
The HCF of 6864,7689 is 33
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 6864/148, 7689/6080?
Answer: GCF of Numerators as per given numbers 6864/148, 7689/6080 is
GCF of Numerators i.e. for 6864,7689 is 33
LCM of denominators i.e. for 148,6080 is 224960.
Thus, GCF of Fractions is 33/224960.Finally, GCF of Fractions for 6864/148, 7689/6080 is 33/224960.