GCF of 32/89, 408/27, 258/35
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 32/89, 408/27, 258/35 i.e 2/84105 easily. The following is the detailed procedure to determine the greatest common factor of fractions 32/89, 408/27, 258/35.
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 32/89,408/27,258/35?
Given fractions are 32/89,408/27,258/35
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 32/89,408/27,258/35, numerators are 32,408,258
Denominators are 89,27,35
The GCF of 32,408,258 is 2 .
LCM of 89,27,35 is 84105.
The greatest common factor of 32/89,408/27,258/35 = [GCF of 32,408,258]/[LCM of 89,27,35]= 2/84105
Therefore, the GCF of 32/89,408/27,258/35 is 2/84105.
To find the highest common factor of 32,408,258, we have to find the factors of both numbers and list the highest common factor.
The factors of 32 are 1, 2, 4, 8, 16, 32
The factors of 408 are 1, 2, 3, 4, 6, 8, 12, 17, 24, 34, 51, 68, 102, 136, 204, 408
The factors of 258 are 1, 2, 3, 6, 43, 86, 129, 258
The HCF of 32,408,258 is 2.
Lets's calculate GCF of 32,408,258
| 2 | 32, 408, 258 |
| 16, 204, 129 |
∴ So the GCF of the given numbers is 2 = 2
Greatest Common Factor of 32,408,258 By Matching Biggest Common Factor Method
Now, list down the factors of 32
:1,2,4,8,16,32
Now, list down the factors of 408
:1,2,3,4,6,8,12,17,24,34,51,68,102,136,204,408
Now, list down the factors of 258
:1,2,3,6,43,86,129,258
Greatest Common Factor
We found the factors 32,408,258 . The biggest common factor number is the GCF number.
So the greatest common factor 32,408,258 is 2.
Lets's calculate LCM of 89,27,35
Given numbers has no common factors except 1. So, there LCM is their product i.e 84105
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 2/84105
Therefore, the GCF of Fractions 32/89,408/27,258/35 is 2/84105
Least Common Multiple of 89,27,35 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 89,27,35 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(89,27,35) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(89,27,35) x common factors =1 x 1 = 1
LCM(89,27,35) = ( 89 × 27 × 35 ) / 1
LCM(89,27,35) = 84105 / 1
LCM(89,27,35) = 84105
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FAQs on GCF of Fractions of 32/89, 408/27, 258/35
1. What is the HCF of 32,408,258?
The HCF of 32,408,258 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 32/89, 408/27, 258/35?
Answer: GCF of Numerators as per given numbers 32/89, 408/27, 258/35 is
GCF of Numerators i.e. for 32,408,258 is 2
LCM of denominators i.e. for 89,27,35 is 84105.
Thus, GCF of Fractions is 2/84105.Finally, GCF of Fractions for 32/89, 408/27, 258/35 is 2/84105.