GCF of 500/24, 750/306
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 500/24, 750/306 i.e 250/1224 easily. The following is the detailed procedure to determine the greatest common factor of fractions 500/24, 750/306.
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 500/24,750/306?
Given fractions are 500/24,750/306
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 500/24,750/306, numerators are 500,750
Denominators are 24,306
The GCF of 500,750 is 250 .
LCM of 24,306 is 1224.
The greatest common factor of 500/24,750/306 = [GCF of 500,750]/[LCM of 24,306]= 250/1224
Therefore, the GCF of 500/24,750/306 is 250/1224.
To find the highest common factor of 500,750, we have to find the factors of both numbers and list the highest common factor.
The factors of 500 are 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500
The factors of 750 are 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 125, 150, 250, 375, 750
The HCF of 500,750 is 250.
Lets's calculate GCF of 500,750
| 2 | 500, 750 |
| 5 | 250, 375 |
| 5 | 50, 75 |
| 5 | 10, 15 |
| 2, 3 |
∴ So the GCF of the given numbers is 2 x 5 x 5 x 5 = 250
Greatest Common Factor of 500,750 By Matching Biggest Common Factor Method
Now, list down the factors of 500
:1,2,4,5,10,20,25,50,100,125,250,500
Now, list down the factors of 750
:1,2,3,5,6,10,15,25,30,50,75,125,150,250,375,750
Greatest Common Factor
We found the factors 500,750 . The biggest common factor number is the GCF number.
So the greatest common factor 500,750 is 250.
Lets's calculate LCM of 24,306
| 2 | 24, 306 |
| 3 | 12, 153 |
| 4, 51 |
∴ So the LCM of the given numbers is 2 x 3 x 4 x 51 = 1224
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 250/1224
Therefore, the GCF of Fractions 500/24,750/306 is 250/1224
Least Common Multiple of 24,306 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 24,306 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(24,306) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(24,306) x common factors =6 x 1 = 6
LCM(24,306) = ( 24 × 306 ) / 6
LCM(24,306) = 7344 / 6
LCM(24,306) = 1224
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FAQs on GCF of Fractions of 500/24, 750/306
1. What is the HCF of 500,750?
The HCF of 500,750 is 250
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 500/24, 750/306?
Answer: GCF of Numerators as per given numbers 500/24, 750/306 is
GCF of Numerators i.e. for 500,750 is 250
LCM of denominators i.e. for 24,306 is 1224.
Thus, GCF of Fractions is 250/1224.Finally, GCF of Fractions for 500/24, 750/306 is 250/1224.