GCF of 40/71, 321/21, 506/36
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 40/71, 321/21, 506/36 i.e 1/17892 easily. The following is the detailed procedure to determine the greatest common factor of fractions 40/71, 321/21, 506/36.
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 40/71,321/21,506/36?
Given fractions are 40/71,321/21,506/36
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 40/71,321/21,506/36, numerators are 40,321,506
Denominators are 71,21,36
The GCF of 40,321,506 is 1 .
LCM of 71,21,36 is 17892.
The greatest common factor of 40/71,321/21,506/36 = [GCF of 40,321,506]/[LCM of 71,21,36]= 1/17892
Therefore, the GCF of 40/71,321/21,506/36 is 1/17892.
To find the highest common factor of 40,321,506, we have to find the factors of both numbers and list the highest common factor.
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
The factors of 321 are 1, 3, 107, 321
The factors of 506 are 1, 2, 11, 22, 23, 46, 253, 506
The HCF of 40,321,506 is 1.
Lets's calculate GCF of 40,321,506
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 40,321,506 By Matching Biggest Common Factor Method
Now, list down the factors of 40
:1,2,4,5,8,10,20,40
Now, list down the factors of 321
:1,3,107,321
Now, list down the factors of 506
:1,2,11,22,23,46,253,506
Greatest Common Factor
We found the factors 40,321,506 . The biggest common factor number is the GCF number.
So the greatest common factor 40,321,506 is 1.
Lets's calculate LCM of 71,21,36
| 3 | 71, 21, 36 |
| 71, 7, 12 |
∴ So the LCM of the given numbers is 3 x 71 x 7 x 12 = 17892
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17892
Therefore, the GCF of Fractions 40/71,321/21,506/36 is 1/17892
Least Common Multiple of 71,21,36 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 71,21,36 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(71,21,36) = 1
common factors(in case of two or more numbers have common factors) = 3
GCF(71,21,36) x common factors =1 x 3 = 3
LCM(71,21,36) = ( 71 × 21 × 36 ) / 3
LCM(71,21,36) = 53676 / 3
LCM(71,21,36) = 17892
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FAQs on GCF of Fractions of 40/71, 321/21, 506/36
1. What is the HCF of 40,321,506?
The HCF of 40,321,506 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 40/71, 321/21, 506/36?
Answer: GCF of Numerators as per given numbers 40/71, 321/21, 506/36 is
GCF of Numerators i.e. for 40,321,506 is 1
LCM of denominators i.e. for 71,21,36 is 17892.
Thus, GCF of Fractions is 1/17892.Finally, GCF of Fractions for 40/71, 321/21, 506/36 is 1/17892.