GCF of 531/68, 180/205
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 531/68, 180/205 i.e 9/13940 easily. The following is the detailed procedure to determine the greatest common factor of fractions 531/68, 180/205.
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 531/68,180/205?
Given fractions are 531/68,180/205
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 531/68,180/205, numerators are 531,180
Denominators are 68,205
The GCF of 531,180 is 9 .
LCM of 68,205 is 13940.
The greatest common factor of 531/68,180/205 = [GCF of 531,180]/[LCM of 68,205]= 9/13940
Therefore, the GCF of 531/68,180/205 is 9/13940.
To find the highest common factor of 531,180, we have to find the factors of both numbers and list the highest common factor.
The factors of 531 are 1, 3, 9, 59, 177, 531
The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
The HCF of 531,180 is 9.
Lets's calculate GCF of 531,180
| 3 | 531, 180 |
| 3 | 177, 60 |
| 59, 20 |
∴ So the GCF of the given numbers is 3 x 3 = 9
Greatest Common Factor of 531,180 By Matching Biggest Common Factor Method
Now, list down the factors of 531
:1,3,9,59,177,531
Now, list down the factors of 180
:1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180
Greatest Common Factor
We found the factors 531,180 . The biggest common factor number is the GCF number.
So the greatest common factor 531,180 is 9.
Lets's calculate LCM of 68,205
Given numbers has no common factors except 1. So, there LCM is their product i.e 13940
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 9/13940
Therefore, the GCF of Fractions 531/68,180/205 is 9/13940
Least Common Multiple of 68,205 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 68,205 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(68,205) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(68,205) x common factors =1 x 1 = 1
LCM(68,205) = ( 68 × 205 ) / 1
LCM(68,205) = 13940 / 1
LCM(68,205) = 13940
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FAQs on GCF of Fractions of 531/68, 180/205
1. What is the HCF of 531,180?
The HCF of 531,180 is 9
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 531/68, 180/205?
Answer: GCF of Numerators as per given numbers 531/68, 180/205 is
GCF of Numerators i.e. for 531,180 is 9
LCM of denominators i.e. for 68,205 is 13940.
Thus, GCF of Fractions is 9/13940.Finally, GCF of Fractions for 531/68, 180/205 is 9/13940.