GCF of 111/31, 765/68, 564/28
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 111/31, 765/68, 564/28 i.e 3/14756 easily. The following is the detailed procedure to determine the greatest common factor of fractions 111/31, 765/68, 564/28.
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 111/31,765/68,564/28?
Given fractions are 111/31,765/68,564/28
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 111/31,765/68,564/28, numerators are 111,765,564
Denominators are 31,68,28
The GCF of 111,765,564 is 3 .
LCM of 31,68,28 is 14756.
The greatest common factor of 111/31,765/68,564/28 = [GCF of 111,765,564]/[LCM of 31,68,28]= 3/14756
Therefore, the GCF of 111/31,765/68,564/28 is 3/14756.
To find the highest common factor of 111,765,564, we have to find the factors of both numbers and list the highest common factor.
The factors of 111 are 1, 3, 37, 111
The factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765
The factors of 564 are 1, 2, 3, 4, 6, 12, 47, 94, 141, 188, 282, 564
The HCF of 111,765,564 is 3.
Lets's calculate GCF of 111,765,564
| 3 | 111, 765, 564 |
| 37, 255, 188 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 111,765,564 By Matching Biggest Common Factor Method
Now, list down the factors of 111
:1,3,37,111
Now, list down the factors of 765
:1,3,5,9,15,17,45,51,85,153,255,765
Now, list down the factors of 564
:1,2,3,4,6,12,47,94,141,188,282,564
Greatest Common Factor
We found the factors 111,765,564 . The biggest common factor number is the GCF number.
So the greatest common factor 111,765,564 is 3.
Lets's calculate LCM of 31,68,28
| 2 | 31, 68, 28 |
| 2 | 31, 34, 14 |
| 31, 17, 7 |
∴ So the LCM of the given numbers is 2 x 2 x 31 x 17 x 7 = 14756
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/14756
Therefore, the GCF of Fractions 111/31,765/68,564/28 is 3/14756
Least Common Multiple of 31,68,28 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 31,68,28 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,68,28) = 1
common factors(in case of two or more numbers have common factors) = 4
GCF(31,68,28) x common factors =1 x 4 = 4
LCM(31,68,28) = ( 31 × 68 × 28 ) / 4
LCM(31,68,28) = 59024 / 4
LCM(31,68,28) = 14756
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FAQs on GCF of Fractions of 111/31, 765/68, 564/28
1. What is the HCF of 111,765,564?
The HCF of 111,765,564 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 111/31, 765/68, 564/28?
Answer: GCF of Numerators as per given numbers 111/31, 765/68, 564/28 is
GCF of Numerators i.e. for 111,765,564 is 3
LCM of denominators i.e. for 31,68,28 is 14756.
Thus, GCF of Fractions is 3/14756.Finally, GCF of Fractions for 111/31, 765/68, 564/28 is 3/14756.