GCF of 498/419, 748/264
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 498/419, 748/264 i.e 2/110616 easily. The following is the detailed procedure to determine the greatest common factor of fractions 498/419, 748/264.
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 498/419,748/264?
Given fractions are 498/419,748/264
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 498/419,748/264, numerators are 498,748
Denominators are 419,264
The GCF of 498,748 is 2 .
LCM of 419,264 is 110616.
The greatest common factor of 498/419,748/264 = [GCF of 498,748]/[LCM of 419,264]= 2/110616
Therefore, the GCF of 498/419,748/264 is 2/110616.
To find the highest common factor of 498,748, 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 748 are 1, 2, 4, 11, 17, 22, 34, 44, 68, 187, 374, 748
The HCF of 498,748 is 2.
Lets's calculate GCF of 498,748
| 2 | 498, 748 |
| 249, 374 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 498,748 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 748
:1,2,4,11,17,22,34,44,68,187,374,748
Greatest Common Factor
We found the factors 498,748 . The biggest common factor number is the GCF number.
So the greatest common factor 498,748 is 2.
Lets's calculate LCM of 419,264
Given numbers has no common factors except 1. So, there LCM is their product i.e 110616
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/110616
Therefore, the GCF of Fractions 498/419,748/264 is 2/110616
Least Common Multiple of 419,264 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 419,264 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(419,264) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(419,264) x common factors =1 x 1 = 1
LCM(419,264) = ( 419 × 264 ) / 1
LCM(419,264) = 110616 / 1
LCM(419,264) = 110616
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FAQs on GCF of Fractions of 498/419, 748/264
1. What is the HCF of 498,748?
The HCF of 498,748 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 498/419, 748/264?
Answer: GCF of Numerators as per given numbers 498/419, 748/264 is
GCF of Numerators i.e. for 498,748 is 2
LCM of denominators i.e. for 419,264 is 110616.
Thus, GCF of Fractions is 2/110616.Finally, GCF of Fractions for 498/419, 748/264 is 2/110616.