GCF of 450/536, 975/210
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 450/536, 975/210 i.e 75/56280 easily. The following is the detailed procedure to determine the greatest common factor of fractions 450/536, 975/210.
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 450/536,975/210?
Given fractions are 450/536,975/210
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 450/536,975/210, numerators are 450,975
Denominators are 536,210
The GCF of 450,975 is 75 .
LCM of 536,210 is 56280.
The greatest common factor of 450/536,975/210 = [GCF of 450,975]/[LCM of 536,210]= 75/56280
Therefore, the GCF of 450/536,975/210 is 75/56280.
To find the highest common factor of 450,975, we have to find the factors of both numbers and list the highest common factor.
The factors of 450 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450
The factors of 975 are 1, 3, 5, 13, 15, 25, 39, 65, 75, 195, 325, 975
The HCF of 450,975 is 75.
Lets's calculate GCF of 450,975
| 3 | 450, 975 |
| 5 | 150, 325 |
| 5 | 30, 65 |
| 6, 13 |
∴ So the GCF of the given numbers is 3 x 5 x 5 = 75
Greatest Common Factor of 450,975 By Matching Biggest Common Factor Method
Now, list down the factors of 450
:1,2,3,5,6,9,10,15,18,25,30,45,50,75,90,150,225,450
Now, list down the factors of 975
:1,3,5,13,15,25,39,65,75,195,325,975
Greatest Common Factor
We found the factors 450,975 . The biggest common factor number is the GCF number.
So the greatest common factor 450,975 is 75.
Lets's calculate LCM of 536,210
| 2 | 536, 210 |
| 268, 105 |
∴ So the LCM of the given numbers is 2 x 268 x 105 = 56280
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 75/56280
Therefore, the GCF of Fractions 450/536,975/210 is 75/56280
Least Common Multiple of 536,210 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 536,210 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(536,210) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(536,210) x common factors =2 x 1 = 2
LCM(536,210) = ( 536 × 210 ) / 2
LCM(536,210) = 112560 / 2
LCM(536,210) = 56280
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FAQs on GCF of Fractions of 450/536, 975/210
1. What is the HCF of 450,975?
The HCF of 450,975 is 75
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 450/536, 975/210?
Answer: GCF of Numerators as per given numbers 450/536, 975/210 is
GCF of Numerators i.e. for 450,975 is 75
LCM of denominators i.e. for 536,210 is 56280.
Thus, GCF of Fractions is 75/56280.Finally, GCF of Fractions for 450/536, 975/210 is 75/56280.