GCF of 507/164, 540/314
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 507/164, 540/314 i.e 3/25748 easily. The following is the detailed procedure to determine the greatest common factor of fractions 507/164, 540/314.
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 507/164,540/314?
Given fractions are 507/164,540/314
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 507/164,540/314, numerators are 507,540
Denominators are 164,314
The GCF of 507,540 is 3 .
LCM of 164,314 is 25748.
The greatest common factor of 507/164,540/314 = [GCF of 507,540]/[LCM of 164,314]= 3/25748
Therefore, the GCF of 507/164,540/314 is 3/25748.
To find the highest common factor of 507,540, we have to find the factors of both numbers and list the highest common factor.
The factors of 507 are 1, 3, 13, 39, 169, 507
The factors of 540 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540
The HCF of 507,540 is 3.
Lets's calculate GCF of 507,540
| 3 | 507, 540 |
| 169, 180 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 507,540 By Matching Biggest Common Factor Method
Now, list down the factors of 507
:1,3,13,39,169,507
Now, list down the factors of 540
:1,2,3,4,5,6,9,10,12,15,18,20,27,30,36,45,54,60,90,108,135,180,270,540
Greatest Common Factor
We found the factors 507,540 . The biggest common factor number is the GCF number.
So the greatest common factor 507,540 is 3.
Lets's calculate LCM of 164,314
| 2 | 164, 314 |
| 82, 157 |
∴ So the LCM of the given numbers is 2 x 82 x 157 = 25748
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/25748
Therefore, the GCF of Fractions 507/164,540/314 is 3/25748
Least Common Multiple of 164,314 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 164,314 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(164,314) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(164,314) x common factors =2 x 1 = 2
LCM(164,314) = ( 164 × 314 ) / 2
LCM(164,314) = 51496 / 2
LCM(164,314) = 25748
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FAQs on GCF of Fractions of 507/164, 540/314
1. What is the HCF of 507,540?
The HCF of 507,540 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 507/164, 540/314?
Answer: GCF of Numerators as per given numbers 507/164, 540/314 is
GCF of Numerators i.e. for 507,540 is 3
LCM of denominators i.e. for 164,314 is 25748.
Thus, GCF of Fractions is 3/25748.Finally, GCF of Fractions for 507/164, 540/314 is 3/25748.