GCF of 87/360, 75/823, 528/745
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 87/360, 75/823, 528/745 i.e 3/44145720 easily. The following is the detailed procedure to determine the greatest common factor of fractions 87/360, 75/823, 528/745.
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 87/360,75/823,528/745?
Given fractions are 87/360,75/823,528/745
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 87/360,75/823,528/745, numerators are 87,75,528
Denominators are 360,823,745
The GCF of 87,75,528 is 3 .
LCM of 360,823,745 is 44145720.
The greatest common factor of 87/360,75/823,528/745 = [GCF of 87,75,528]/[LCM of 360,823,745]= 3/44145720
Therefore, the GCF of 87/360,75/823,528/745 is 3/44145720.
To find the highest common factor of 87,75,528, we have to find the factors of both numbers and list the highest common factor.
The factors of 87 are 1, 3, 29, 87
The factors of 75 are 1, 3, 5, 15, 25, 75
The factors of 528 are 1, 2, 3, 4, 6, 8, 11, 12, 16, 22, 24, 33, 44, 48, 66, 88, 132, 176, 264, 528
The HCF of 87,75,528 is 3.
Lets's calculate GCF of 87,75,528
| 3 | 87, 75, 528 |
| 29, 25, 176 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 87,75,528 By Matching Biggest Common Factor Method
Now, list down the factors of 87
:1,3,29,87
Now, list down the factors of 75
:1,3,5,15,25,75
Now, list down the factors of 528
:1,2,3,4,6,8,11,12,16,22,24,33,44,48,66,88,132,176,264,528
Greatest Common Factor
We found the factors 87,75,528 . The biggest common factor number is the GCF number.
So the greatest common factor 87,75,528 is 3.
Lets's calculate LCM of 360,823,745
| 5 | 360, 823, 745 |
| 72, 823, 149 |
∴ So the LCM of the given numbers is 5 x 72 x 823 x 149 = 44145720
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/44145720
Therefore, the GCF of Fractions 87/360,75/823,528/745 is 3/44145720
Least Common Multiple of 360,823,745 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 360,823,745 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(360,823,745) = 1
common factors(in case of two or more numbers have common factors) = 5
GCF(360,823,745) x common factors =1 x 5 = 5
LCM(360,823,745) = ( 360 × 823 × 745 ) / 5
LCM(360,823,745) = 220728600 / 5
LCM(360,823,745) = 44145720
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FAQs on GCF of Fractions of 87/360, 75/823, 528/745
1. What is the HCF of 87,75,528?
The HCF of 87,75,528 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 87/360, 75/823, 528/745?
Answer: GCF of Numerators as per given numbers 87/360, 75/823, 528/745 is
GCF of Numerators i.e. for 87,75,528 is 3
LCM of denominators i.e. for 360,823,745 is 44145720.
Thus, GCF of Fractions is 3/44145720.Finally, GCF of Fractions for 87/360, 75/823, 528/745 is 3/44145720.