GCF of 542/421, 782/497
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 542/421, 782/497 i.e 2/209237 easily. The following is the detailed procedure to determine the greatest common factor of fractions 542/421, 782/497.
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 542/421,782/497?
Given fractions are 542/421,782/497
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 542/421,782/497, numerators are 542,782
Denominators are 421,497
The GCF of 542,782 is 2 .
LCM of 421,497 is 209237.
The greatest common factor of 542/421,782/497 = [GCF of 542,782]/[LCM of 421,497]= 2/209237
Therefore, the GCF of 542/421,782/497 is 2/209237.
To find the highest common factor of 542,782, we have to find the factors of both numbers and list the highest common factor.
The factors of 542 are 1, 2, 271, 542
The factors of 782 are 1, 2, 17, 23, 34, 46, 391, 782
The HCF of 542,782 is 2.
Lets's calculate GCF of 542,782
| 2 | 542, 782 |
| 271, 391 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 542,782 By Matching Biggest Common Factor Method
Now, list down the factors of 542
:1,2,271,542
Now, list down the factors of 782
:1,2,17,23,34,46,391,782
Greatest Common Factor
We found the factors 542,782 . The biggest common factor number is the GCF number.
So the greatest common factor 542,782 is 2.
Lets's calculate LCM of 421,497
Given numbers has no common factors except 1. So, there LCM is their product i.e 209237
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/209237
Therefore, the GCF of Fractions 542/421,782/497 is 2/209237
Least Common Multiple of 421,497 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 421,497 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(421,497) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(421,497) x common factors =1 x 1 = 1
LCM(421,497) = ( 421 × 497 ) / 1
LCM(421,497) = 209237 / 1
LCM(421,497) = 209237
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FAQs on GCF of Fractions of 542/421, 782/497
1. What is the HCF of 542,782?
The HCF of 542,782 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 542/421, 782/497?
Answer: GCF of Numerators as per given numbers 542/421, 782/497 is
GCF of Numerators i.e. for 542,782 is 2
LCM of denominators i.e. for 421,497 is 209237.
Thus, GCF of Fractions is 2/209237.Finally, GCF of Fractions for 542/421, 782/497 is 2/209237.