GCF of 52/76, 24/31, 99/52, 87/31
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 52/76, 24/31, 99/52, 87/31 i.e 1/30628 easily. The following is the detailed procedure to determine the greatest common factor of fractions 52/76, 24/31, 99/52, 87/31.
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 52/76,24/31,99/52,87/31?
Given fractions are 52/76,24/31,99/52,87/31
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 52/76,24/31,99/52,87/31, numerators are 52,24,99,87
Denominators are 76,31,52,31
The GCF of 52,24,99,87 is 1 .
LCM of 76,31,52,31 is 30628.
The greatest common factor of 52/76,24/31,99/52,87/31 = [GCF of 52,24,99,87]/[LCM of 76,31,52,31]= 1/30628
Therefore, the GCF of 52/76,24/31,99/52,87/31 is 1/30628.
To find the highest common factor of 52,24,99,87, we have to find the factors of both numbers and list the highest common factor.
The factors of 52 are 1, 2, 4, 13, 26, 52
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
The factors of 99 are 1, 3, 9, 11, 33, 99
The factors of 87 are 1, 3, 29, 87
The HCF of 52,24,99,87 is 1.
Lets's calculate GCF of 52,24,99,87
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 52,24,99,87 By Matching Biggest Common Factor Method
Now, list down the factors of 52
:1,2,4,13,26,52
Now, list down the factors of 24
:1,2,3,4,6,8,12,24
Now, list down the factors of 99
:1,3,9,11,33,99
Now, list down the factors of 87
:1,3,29,87
Greatest Common Factor
We found the factors 52,24,99,87 . The biggest common factor number is the GCF number.
So the greatest common factor 52,24,99,87 is 1.
Lets's calculate LCM of 76,31,52,31
| 2 | 76, 31, 52, 31 |
| 2 | 38, 31, 26, 31 |
| 31 | 19, 31, 13, 31 |
| 19, 1, 13, 1 |
∴ So the LCM of the given numbers is 2 x 2 x 31 x 19 x 1 x 13 x 1 = 30628
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/30628
Therefore, the GCF of Fractions 52/76,24/31,99/52,87/31 is 1/30628
Least Common Multiple of 76,31,52,31 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 76,31,52,31 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(76,31,52,31) = 1
common factors(in case of two or more numbers have common factors) = 124
GCF(76,31,52,31) x common factors =1 x 124 = 124
LCM(76,31,52,31) = ( 76 × 31 × 52 × 31 ) / 124
LCM(76,31,52,31) = 3797872 / 124
LCM(76,31,52,31) = 30628
GCF of Fractions Calculation Examples
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FAQs on GCF of Fractions of 52/76, 24/31, 99/52, 87/31
1. What is the HCF of 52,24,99,87?
The HCF of 52,24,99,87 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 52/76, 24/31, 99/52, 87/31?
Answer: GCF of Numerators as per given numbers 52/76, 24/31, 99/52, 87/31 is
GCF of Numerators i.e. for 52,24,99,87 is 1
LCM of denominators i.e. for 76,31,52,31 is 30628.
Thus, GCF of Fractions is 1/30628.Finally, GCF of Fractions for 52/76, 24/31, 99/52, 87/31 is 1/30628.