GCF of 711/21, 498/546
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 711/21, 498/546 i.e 3/546 easily. The following is the detailed procedure to determine the greatest common factor of fractions 711/21, 498/546.
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 711/21,498/546?
Given fractions are 711/21,498/546
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 711/21,498/546, numerators are 711,498
Denominators are 21,546
The GCF of 711,498 is 3 .
LCM of 21,546 is 546.
The greatest common factor of 711/21,498/546 = [GCF of 711,498]/[LCM of 21,546]= 3/546
Therefore, the GCF of 711/21,498/546 is 3/546.
To find the highest common factor of 711,498, we have to find the factors of both numbers and list the highest common factor.
The factors of 711 are 1, 3, 9, 79, 237, 711
The factors of 498 are 1, 2, 3, 6, 83, 166, 249, 498
The HCF of 711,498 is 3.
Lets's calculate GCF of 711,498
| 3 | 711, 498 |
| 237, 166 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 711,498 By Matching Biggest Common Factor Method
Now, list down the factors of 711
:1,3,9,79,237,711
Now, list down the factors of 498
:1,2,3,6,83,166,249,498
Greatest Common Factor
We found the factors 711,498 . The biggest common factor number is the GCF number.
So the greatest common factor 711,498 is 3.
Lets's calculate LCM of 21,546
| 3 | 21, 546 |
| 7 | 7, 182 |
| 1, 26 |
∴ So the LCM of the given numbers is 3 x 7 x 1 x 26 = 546
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/546
Therefore, the GCF of Fractions 711/21,498/546 is 3/546
Least Common Multiple of 21,546 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 21,546 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(21,546) = 21
common factors(in case of two or more numbers have common factors) = 1
GCF(21,546) x common factors =21 x 1 = 21
LCM(21,546) = ( 21 × 546 ) / 21
LCM(21,546) = 11466 / 21
LCM(21,546) = 546
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FAQs on GCF of Fractions of 711/21, 498/546
1. What is the HCF of 711,498?
The HCF of 711,498 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 711/21, 498/546?
Answer: GCF of Numerators as per given numbers 711/21, 498/546 is
GCF of Numerators i.e. for 711,498 is 3
LCM of denominators i.e. for 21,546 is 546.
Thus, GCF of Fractions is 3/546.Finally, GCF of Fractions for 711/21, 498/546 is 3/546.