GCF of 498/31, 534/7781
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 498/31, 534/7781 i.e 6/7781 easily. The following is the detailed procedure to determine the greatest common factor of fractions 498/31, 534/7781.
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 498/31,534/7781?
Given fractions are 498/31,534/7781
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 498/31,534/7781, numerators are 498,534
Denominators are 31,7781
The GCF of 498,534 is 6 .
LCM of 31,7781 is 7781.
The greatest common factor of 498/31,534/7781 = [GCF of 498,534]/[LCM of 31,7781]= 6/7781
Therefore, the GCF of 498/31,534/7781 is 6/7781.
To find the highest common factor of 498,534, 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 534 are 1, 2, 3, 6, 89, 178, 267, 534
The HCF of 498,534 is 6.
Lets's calculate GCF of 498,534
| 2 | 498, 534 |
| 3 | 249, 267 |
| 83, 89 |
∴ So the GCF of the given numbers is 2 x 3 = 6
Greatest Common Factor of 498,534 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 534
:1,2,3,6,89,178,267,534
Greatest Common Factor
We found the factors 498,534 . The biggest common factor number is the GCF number.
So the greatest common factor 498,534 is 6.
Lets's calculate LCM of 31,7781
| 31 | 31, 7781 |
| 1, 251 |
∴ So the LCM of the given numbers is 31 x 1 x 251 = 7781
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 6/7781
Therefore, the GCF of Fractions 498/31,534/7781 is 6/7781
Least Common Multiple of 31,7781 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 31,7781 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(31,7781) = 31
common factors(in case of two or more numbers have common factors) = 1
GCF(31,7781) x common factors =31 x 1 = 31
LCM(31,7781) = ( 31 × 7781 ) / 31
LCM(31,7781) = 241211 / 31
LCM(31,7781) = 7781
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FAQs on GCF of Fractions of 498/31, 534/7781
1. What is the HCF of 498,534?
The HCF of 498,534 is 6
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 498/31, 534/7781?
Answer: GCF of Numerators as per given numbers 498/31, 534/7781 is
GCF of Numerators i.e. for 498,534 is 6
LCM of denominators i.e. for 31,7781 is 7781.
Thus, GCF of Fractions is 6/7781.Finally, GCF of Fractions for 498/31, 534/7781 is 6/7781.