GCF of 7275/678, 6156/5667
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 7275/678, 6156/5667 i.e 3/1280742 easily. The following is the detailed procedure to determine the greatest common factor of fractions 7275/678, 6156/5667.
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 7275/678,6156/5667?
Given fractions are 7275/678,6156/5667
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 7275/678,6156/5667, numerators are 7275,6156
Denominators are 678,5667
The GCF of 7275,6156 is 3 .
LCM of 678,5667 is 1280742.
The greatest common factor of 7275/678,6156/5667 = [GCF of 7275,6156]/[LCM of 678,5667]= 3/1280742
Therefore, the GCF of 7275/678,6156/5667 is 3/1280742.
To find the highest common factor of 7275,6156, we have to find the factors of both numbers and list the highest common factor.
The factors of 7275 are 1, 3, 5, 15, 25, 75, 97, 291, 485, 1455, 2425, 7275
The factors of 6156 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 27, 36, 38, 54, 57, 76, 81, 108, 114, 162, 171, 228, 324, 342, 513, 684, 1026, 1539, 2052, 3078, 6156
The HCF of 7275,6156 is 3.
Lets's calculate GCF of 7275,6156
| 3 | 7275, 6156 |
| 2425, 2052 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 7275,6156 By Matching Biggest Common Factor Method
Now, list down the factors of 7275
:1,3,5,15,25,75,97,291,485,1455,2425,7275
Now, list down the factors of 6156
:1,2,3,4,6,9,12,18,19,27,36,38,54,57,76,81,108,114,162,171,228,324,342,513,684,1026,1539,2052,3078,6156
Greatest Common Factor
We found the factors 7275,6156 . The biggest common factor number is the GCF number.
So the greatest common factor 7275,6156 is 3.
Lets's calculate LCM of 678,5667
| 3 | 678, 5667 |
| 226, 1889 |
∴ So the LCM of the given numbers is 3 x 226 x 1889 = 1280742
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/1280742
Therefore, the GCF of Fractions 7275/678,6156/5667 is 3/1280742
Least Common Multiple of 678,5667 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 678,5667 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(678,5667) = 3
common factors(in case of two or more numbers have common factors) = 1
GCF(678,5667) x common factors =3 x 1 = 3
LCM(678,5667) = ( 678 × 5667 ) / 3
LCM(678,5667) = 3842226 / 3
LCM(678,5667) = 1280742
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FAQs on GCF of Fractions of 7275/678, 6156/5667
1. What is the HCF of 7275,6156?
The HCF of 7275,6156 is 3
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 7275/678, 6156/5667?
Answer: GCF of Numerators as per given numbers 7275/678, 6156/5667 is
GCF of Numerators i.e. for 7275,6156 is 3
LCM of denominators i.e. for 678,5667 is 1280742.
Thus, GCF of Fractions is 3/1280742.Finally, GCF of Fractions for 7275/678, 6156/5667 is 3/1280742.