GCF of 450/542, 310/174
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 450/542, 310/174 i.e 10/47154 easily. The following is the detailed procedure to determine the greatest common factor of fractions 450/542, 310/174.
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 450/542,310/174?
Given fractions are 450/542,310/174
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 450/542,310/174, numerators are 450,310
Denominators are 542,174
The GCF of 450,310 is 10 .
LCM of 542,174 is 47154.
The greatest common factor of 450/542,310/174 = [GCF of 450,310]/[LCM of 542,174]= 10/47154
Therefore, the GCF of 450/542,310/174 is 10/47154.
To find the highest common factor of 450,310, 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 310 are 1, 2, 5, 10, 31, 62, 155, 310
The HCF of 450,310 is 10.
Lets's calculate GCF of 450,310
| 2 | 450, 310 |
| 5 | 225, 155 |
| 45, 31 |
∴ So the GCF of the given numbers is 2 x 5 = 10
Greatest Common Factor of 450,310 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 310
:1,2,5,10,31,62,155,310
Greatest Common Factor
We found the factors 450,310 . The biggest common factor number is the GCF number.
So the greatest common factor 450,310 is 10.
Lets's calculate LCM of 542,174
| 2 | 542, 174 |
| 271, 87 |
∴ So the LCM of the given numbers is 2 x 271 x 87 = 47154
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 10/47154
Therefore, the GCF of Fractions 450/542,310/174 is 10/47154
Least Common Multiple of 542,174 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 542,174 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(542,174) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(542,174) x common factors =2 x 1 = 2
LCM(542,174) = ( 542 × 174 ) / 2
LCM(542,174) = 94308 / 2
LCM(542,174) = 47154
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FAQs on GCF of Fractions of 450/542, 310/174
1. What is the HCF of 450,310?
The HCF of 450,310 is 10
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 450/542, 310/174?
Answer: GCF of Numerators as per given numbers 450/542, 310/174 is
GCF of Numerators i.e. for 450,310 is 10
LCM of denominators i.e. for 542,174 is 47154.
Thus, GCF of Fractions is 10/47154.Finally, GCF of Fractions for 450/542, 310/174 is 10/47154.