GCF of 498/182, 512/210
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 498/182, 512/210 i.e 2/2730 easily. The following is the detailed procedure to determine the greatest common factor of fractions 498/182, 512/210.
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 498/182,512/210?
Given fractions are 498/182,512/210
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 498/182,512/210, numerators are 498,512
Denominators are 182,210
The GCF of 498,512 is 2 .
LCM of 182,210 is 2730.
The greatest common factor of 498/182,512/210 = [GCF of 498,512]/[LCM of 182,210]= 2/2730
Therefore, the GCF of 498/182,512/210 is 2/2730.
To find the highest common factor of 498,512, we have to find the factors of both numbers and list the highest common factor.
The factors of 498 are 1, 2, 3, 6, 83, 166, 249, 498
The factors of 512 are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512
The HCF of 498,512 is 2.
Lets's calculate GCF of 498,512
| 2 | 498, 512 |
| 249, 256 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 498,512 By Matching Biggest Common Factor Method
Now, list down the factors of 498
:1,2,3,6,83,166,249,498
Now, list down the factors of 512
:1,2,4,8,16,32,64,128,256,512
Greatest Common Factor
We found the factors 498,512 . The biggest common factor number is the GCF number.
So the greatest common factor 498,512 is 2.
Lets's calculate LCM of 182,210
| 2 | 182, 210 |
| 7 | 91, 105 |
| 13, 15 |
∴ So the LCM of the given numbers is 2 x 7 x 13 x 15 = 2730
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/2730
Therefore, the GCF of Fractions 498/182,512/210 is 2/2730
Least Common Multiple of 182,210 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 182,210 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(182,210) = 14
common factors(in case of two or more numbers have common factors) = 1
GCF(182,210) x common factors =14 x 1 = 14
LCM(182,210) = ( 182 × 210 ) / 14
LCM(182,210) = 38220 / 14
LCM(182,210) = 2730
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 498/182, 512/210
1. What is the HCF of 498,512?
The HCF of 498,512 is 2
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 498/182, 512/210?
Answer: GCF of Numerators as per given numbers 498/182, 512/210 is
GCF of Numerators i.e. for 498,512 is 2
LCM of denominators i.e. for 182,210 is 2730.
Thus, GCF of Fractions is 2/2730.Finally, GCF of Fractions for 498/182, 512/210 is 2/2730.