GCF of 22/312, 40/405, 705/842
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 22/312, 40/405, 705/842 i.e 1/17732520 easily. The following is the detailed procedure to determine the greatest common factor of fractions 22/312, 40/405, 705/842.
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 22/312,40/405,705/842?
Given fractions are 22/312,40/405,705/842
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 22/312,40/405,705/842, numerators are 22,40,705
Denominators are 312,405,842
The GCF of 22,40,705 is 1 .
LCM of 312,405,842 is 17732520.
The greatest common factor of 22/312,40/405,705/842 = [GCF of 22,40,705]/[LCM of 312,405,842]= 1/17732520
Therefore, the GCF of 22/312,40/405,705/842 is 1/17732520.
To find the highest common factor of 22,40,705, we have to find the factors of both numbers and list the highest common factor.
The factors of 22 are 1, 2, 11, 22
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40
The factors of 705 are 1, 3, 5, 15, 47, 141, 235, 705
The HCF of 22,40,705 is 1.
Lets's calculate GCF of 22,40,705
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 22,40,705 By Matching Biggest Common Factor Method
Now, list down the factors of 22
:1,2,11,22
Now, list down the factors of 40
:1,2,4,5,8,10,20,40
Now, list down the factors of 705
:1,3,5,15,47,141,235,705
Greatest Common Factor
We found the factors 22,40,705 . The biggest common factor number is the GCF number.
So the greatest common factor 22,40,705 is 1.
Lets's calculate LCM of 312,405,842
| 2 | 312, 405, 842 |
| 3 | 156, 405, 421 |
| 52, 135, 421 |
∴ So the LCM of the given numbers is 2 x 3 x 52 x 135 x 421 = 17732520
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/17732520
Therefore, the GCF of Fractions 22/312,40/405,705/842 is 1/17732520
Least Common Multiple of 312,405,842 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 312,405,842 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(312,405,842) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(312,405,842) x common factors =1 x 6 = 6
LCM(312,405,842) = ( 312 × 405 × 842 ) / 6
LCM(312,405,842) = 106395120 / 6
LCM(312,405,842) = 17732520
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FAQs on GCF of Fractions of 22/312, 40/405, 705/842
1. What is the HCF of 22,40,705?
The HCF of 22,40,705 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 22/312, 40/405, 705/842?
Answer: GCF of Numerators as per given numbers 22/312, 40/405, 705/842 is
GCF of Numerators i.e. for 22,40,705 is 1
LCM of denominators i.e. for 312,405,842 is 17732520.
Thus, GCF of Fractions is 1/17732520.Finally, GCF of Fractions for 22/312, 40/405, 705/842 is 1/17732520.