GCF of 731/42, 212/306
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 731/42, 212/306 i.e 1/2142 easily. The following is the detailed procedure to determine the greatest common factor of fractions 731/42, 212/306.
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 731/42,212/306?
Given fractions are 731/42,212/306
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 731/42,212/306, numerators are 731,212
Denominators are 42,306
The GCF of 731,212 is 1 .
LCM of 42,306 is 2142.
The greatest common factor of 731/42,212/306 = [GCF of 731,212]/[LCM of 42,306]= 1/2142
Therefore, the GCF of 731/42,212/306 is 1/2142.
To find the highest common factor of 731,212, we have to find the factors of both numbers and list the highest common factor.
The factors of 731 are 1, 17, 43, 731
The factors of 212 are 1, 2, 4, 53, 106, 212
The HCF of 731,212 is 1.
Lets's calculate GCF of 731,212
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 731,212 By Matching Biggest Common Factor Method
Now, list down the factors of 731
:1,17,43,731
Now, list down the factors of 212
:1,2,4,53,106,212
Greatest Common Factor
We found the factors 731,212 . The biggest common factor number is the GCF number.
So the greatest common factor 731,212 is 1.
Lets's calculate LCM of 42,306
| 2 | 42, 306 |
| 3 | 21, 153 |
| 7, 51 |
∴ So the LCM of the given numbers is 2 x 3 x 7 x 51 = 2142
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/2142
Therefore, the GCF of Fractions 731/42,212/306 is 1/2142
Least Common Multiple of 42,306 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 42,306 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,306) = 6
common factors(in case of two or more numbers have common factors) = 1
GCF(42,306) x common factors =6 x 1 = 6
LCM(42,306) = ( 42 × 306 ) / 6
LCM(42,306) = 12852 / 6
LCM(42,306) = 2142
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FAQs on GCF of Fractions of 731/42, 212/306
1. What is the HCF of 731,212?
The HCF of 731,212 is 1
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 731/42, 212/306?
Answer: GCF of Numerators as per given numbers 731/42, 212/306 is
GCF of Numerators i.e. for 731,212 is 1
LCM of denominators i.e. for 42,306 is 2142.
Thus, GCF of Fractions is 1/2142.Finally, GCF of Fractions for 731/42, 212/306 is 1/2142.