GCF of 493/120, 524/162
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 493/120, 524/162 i.e 1/3240 easily. The following is the detailed procedure to determine the greatest common factor of fractions 493/120, 524/162.
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 493/120,524/162?
Given fractions are 493/120,524/162
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 493/120,524/162, numerators are 493,524
Denominators are 120,162
The GCF of 493,524 is 1 .
LCM of 120,162 is 3240.
The greatest common factor of 493/120,524/162 = [GCF of 493,524]/[LCM of 120,162]= 1/3240
Therefore, the GCF of 493/120,524/162 is 1/3240.
To find the highest common factor of 493,524, we have to find the factors of both numbers and list the highest common factor.
The factors of 493 are 1, 17, 29, 493
The factors of 524 are 1, 2, 4, 131, 262, 524
The HCF of 493,524 is 1.
Lets's calculate GCF of 493,524
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 493,524 By Matching Biggest Common Factor Method
Now, list down the factors of 493
:1,17,29,493
Now, list down the factors of 524
:1,2,4,131,262,524
Greatest Common Factor
We found the factors 493,524 . The biggest common factor number is the GCF number.
So the greatest common factor 493,524 is 1.
Lets's calculate LCM of 120,162
| 2 | 120, 162 |
| 3 | 60, 81 |
| 20, 27 |
∴ So the LCM of the given numbers is 2 x 3 x 20 x 27 = 3240
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/3240
Therefore, the GCF of Fractions 493/120,524/162 is 1/3240
Least Common Multiple of 120,162 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 120,162 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(120,162) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(120,162) x common factors =6 x 1 = 6
LCM(120,162) = ( 120 × 162 ) / 6
LCM(120,162) = 19440 / 6
LCM(120,162) = 3240
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FAQs on GCF of Fractions of 493/120, 524/162
1. What is the HCF of 493,524?
The HCF of 493,524 is 1
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 493/120, 524/162?
Answer: GCF of Numerators as per given numbers 493/120, 524/162 is
GCF of Numerators i.e. for 493,524 is 1
LCM of denominators i.e. for 120,162 is 3240.
Thus, GCF of Fractions is 1/3240.Finally, GCF of Fractions for 493/120, 524/162 is 1/3240.