GCF of 52/18, 74/22, 214/585
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 52/18, 74/22, 214/585 i.e 2/12870 easily. The following is the detailed procedure to determine the greatest common factor of fractions 52/18, 74/22, 214/585.
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 52/18,74/22,214/585?
Given fractions are 52/18,74/22,214/585
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 52/18,74/22,214/585, numerators are 52,74,214
Denominators are 18,22,585
The GCF of 52,74,214 is 2 .
LCM of 18,22,585 is 12870.
The greatest common factor of 52/18,74/22,214/585 = [GCF of 52,74,214]/[LCM of 18,22,585]= 2/12870
Therefore, the GCF of 52/18,74/22,214/585 is 2/12870.
To find the highest common factor of 52,74,214, we have to find the factors of both numbers and list the highest common factor.
The factors of 52 are 1, 2, 4, 13, 26, 52
The factors of 74 are 1, 2, 37, 74
The factors of 214 are 1, 2, 107, 214
The HCF of 52,74,214 is 2.
Lets's calculate GCF of 52,74,214
| 2 | 52, 74, 214 |
| 26, 37, 107 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 52,74,214 By Matching Biggest Common Factor Method
Now, list down the factors of 52
:1,2,4,13,26,52
Now, list down the factors of 74
:1,2,37,74
Now, list down the factors of 214
:1,2,107,214
Greatest Common Factor
We found the factors 52,74,214 . The biggest common factor number is the GCF number.
So the greatest common factor 52,74,214 is 2.
Lets's calculate LCM of 18,22,585
| 2 | 18, 22, 585 |
| 3 | 9, 11, 585 |
| 3 | 3, 11, 195 |
| 1, 11, 65 |
∴ So the LCM of the given numbers is 2 x 3 x 3 x 1 x 11 x 65 = 12870
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/12870
Therefore, the GCF of Fractions 52/18,74/22,214/585 is 2/12870
Least Common Multiple of 18,22,585 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 18,22,585 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(18,22,585) = 1
common factors(in case of two or more numbers have common factors) = 18
GCF(18,22,585) x common factors =1 x 18 = 18
LCM(18,22,585) = ( 18 × 22 × 585 ) / 18
LCM(18,22,585) = 231660 / 18
LCM(18,22,585) = 12870
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FAQs on GCF of Fractions of 52/18, 74/22, 214/585
1. What is the HCF of 52,74,214?
The HCF of 52,74,214 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 52/18, 74/22, 214/585?
Answer: GCF of Numerators as per given numbers 52/18, 74/22, 214/585 is
GCF of Numerators i.e. for 52,74,214 is 2
LCM of denominators i.e. for 18,22,585 is 12870.
Thus, GCF of Fractions is 2/12870.Finally, GCF of Fractions for 52/18, 74/22, 214/585 is 2/12870.