GCF of 567/12, 684/75, 923/76
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 567/12, 684/75, 923/76 i.e 1/5700 easily. The following is the detailed procedure to determine the greatest common factor of fractions 567/12, 684/75, 923/76.
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 567/12,684/75,923/76?
Given fractions are 567/12,684/75,923/76
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 567/12,684/75,923/76, numerators are 567,684,923
Denominators are 12,75,76
The GCF of 567,684,923 is 1 .
LCM of 12,75,76 is 5700.
The greatest common factor of 567/12,684/75,923/76 = [GCF of 567,684,923]/[LCM of 12,75,76]= 1/5700
Therefore, the GCF of 567/12,684/75,923/76 is 1/5700.
To find the highest common factor of 567,684,923, we have to find the factors of both numbers and list the highest common factor.
The factors of 567 are 1, 3, 7, 9, 21, 27, 63, 81, 189, 567
The factors of 684 are 1, 2, 3, 4, 6, 9, 12, 18, 19, 36, 38, 57, 76, 114, 171, 228, 342, 684
The factors of 923 are 1, 13, 71, 923
The HCF of 567,684,923 is 1.
Lets's calculate GCF of 567,684,923
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 567,684,923 By Matching Biggest Common Factor Method
Now, list down the factors of 567
:1,3,7,9,21,27,63,81,189,567
Now, list down the factors of 684
:1,2,3,4,6,9,12,18,19,36,38,57,76,114,171,228,342,684
Now, list down the factors of 923
:1,13,71,923
Greatest Common Factor
We found the factors 567,684,923 . The biggest common factor number is the GCF number.
So the greatest common factor 567,684,923 is 1.
Lets's calculate LCM of 12,75,76
| 2 | 12, 75, 76 |
| 2 | 6, 75, 38 |
| 3 | 3, 75, 19 |
| 1, 25, 19 |
∴ So the LCM of the given numbers is 2 x 2 x 3 x 1 x 25 x 19 = 5700
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/5700
Therefore, the GCF of Fractions 567/12,684/75,923/76 is 1/5700
Least Common Multiple of 12,75,76 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 12,75,76 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(12,75,76) = 1
common factors(in case of two or more numbers have common factors) = 12
GCF(12,75,76) x common factors =1 x 12 = 12
LCM(12,75,76) = ( 12 × 75 × 76 ) / 12
LCM(12,75,76) = 68400 / 12
LCM(12,75,76) = 5700
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FAQs on GCF of Fractions of 567/12, 684/75, 923/76
1. What is the HCF of 567,684,923?
The HCF of 567,684,923 is 1
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 567/12, 684/75, 923/76?
Answer: GCF of Numerators as per given numbers 567/12, 684/75, 923/76 is
GCF of Numerators i.e. for 567,684,923 is 1
LCM of denominators i.e. for 12,75,76 is 5700.
Thus, GCF of Fractions is 1/5700.Finally, GCF of Fractions for 567/12, 684/75, 923/76 is 1/5700.