GCF of 32/45, 49/10, 205/321
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 32/45, 49/10, 205/321 i.e 1/9630 easily. The following is the detailed procedure to determine the greatest common factor of fractions 32/45, 49/10, 205/321.
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 32/45,49/10,205/321?
Given fractions are 32/45,49/10,205/321
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 32/45,49/10,205/321, numerators are 32,49,205
Denominators are 45,10,321
The GCF of 32,49,205 is 1 .
LCM of 45,10,321 is 9630.
The greatest common factor of 32/45,49/10,205/321 = [GCF of 32,49,205]/[LCM of 45,10,321]= 1/9630
Therefore, the GCF of 32/45,49/10,205/321 is 1/9630.
To find the highest common factor of 32,49,205, 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 49 are 1, 7, 49
The factors of 205 are 1, 5, 41, 205
The HCF of 32,49,205 is 1.
Lets's calculate GCF of 32,49,205
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 32,49,205 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 49
:1,7,49
Now, list down the factors of 205
:1,5,41,205
Greatest Common Factor
We found the factors 32,49,205 . The biggest common factor number is the GCF number.
So the greatest common factor 32,49,205 is 1.
Lets's calculate LCM of 45,10,321
| 3 | 45, 10, 321 |
| 5 | 15, 10, 107 |
| 3, 2, 107 |
∴ So the LCM of the given numbers is 3 x 5 x 3 x 2 x 107 = 9630
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/9630
Therefore, the GCF of Fractions 32/45,49/10,205/321 is 1/9630
Least Common Multiple of 45,10,321 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 45,10,321 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(45,10,321) = 1
common factors(in case of two or more numbers have common factors) = 15
GCF(45,10,321) x common factors =1 x 15 = 15
LCM(45,10,321) = ( 45 × 10 × 321 ) / 15
LCM(45,10,321) = 144450 / 15
LCM(45,10,321) = 9630
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FAQs on GCF of Fractions of 32/45, 49/10, 205/321
1. What is the HCF of 32,49,205?
The HCF of 32,49,205 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 32/45, 49/10, 205/321?
Answer: GCF of Numerators as per given numbers 32/45, 49/10, 205/321 is
GCF of Numerators i.e. for 32,49,205 is 1
LCM of denominators i.e. for 45,10,321 is 9630.
Thus, GCF of Fractions is 1/9630.Finally, GCF of Fractions for 32/45, 49/10, 205/321 is 1/9630.