GCF of 909/42, 969/65, 732/15
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 909/42, 969/65, 732/15 i.e 3/2730 easily. The following is the detailed procedure to determine the greatest common factor of fractions 909/42, 969/65, 732/15.
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 909/42,969/65,732/15?
Given fractions are 909/42,969/65,732/15
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 909/42,969/65,732/15, numerators are 909,969,732
Denominators are 42,65,15
The GCF of 909,969,732 is 3 .
LCM of 42,65,15 is 2730.
The greatest common factor of 909/42,969/65,732/15 = [GCF of 909,969,732]/[LCM of 42,65,15]= 3/2730
Therefore, the GCF of 909/42,969/65,732/15 is 3/2730.
To find the highest common factor of 909,969,732, we have to find the factors of both numbers and list the highest common factor.
The factors of 909 are 1, 3, 9, 101, 303, 909
The factors of 969 are 1, 3, 17, 19, 51, 57, 323, 969
The factors of 732 are 1, 2, 3, 4, 6, 12, 61, 122, 183, 244, 366, 732
The HCF of 909,969,732 is 3.
Lets's calculate GCF of 909,969,732
| 3 | 909, 969, 732 |
| 303, 323, 244 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 909,969,732 By Matching Biggest Common Factor Method
Now, list down the factors of 909
:1,3,9,101,303,909
Now, list down the factors of 969
:1,3,17,19,51,57,323,969
Now, list down the factors of 732
:1,2,3,4,6,12,61,122,183,244,366,732
Greatest Common Factor
We found the factors 909,969,732 . The biggest common factor number is the GCF number.
So the greatest common factor 909,969,732 is 3.
Lets's calculate LCM of 42,65,15
| 3 | 42, 65, 15 |
| 5 | 14, 65, 5 |
| 14, 13, 1 |
∴ So the LCM of the given numbers is 3 x 5 x 14 x 13 x 1 = 2730
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/2730
Therefore, the GCF of Fractions 909/42,969/65,732/15 is 3/2730
Least Common Multiple of 42,65,15 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 42,65,15 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(42,65,15) = 1
common factors(in case of two or more numbers have common factors) = 15
GCF(42,65,15) x common factors =1 x 15 = 15
LCM(42,65,15) = ( 42 × 65 × 15 ) / 15
LCM(42,65,15) = 40950 / 15
LCM(42,65,15) = 2730
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FAQs on GCF of Fractions of 909/42, 969/65, 732/15
1. What is the HCF of 909,969,732?
The HCF of 909,969,732 is 3
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 909/42, 969/65, 732/15?
Answer: GCF of Numerators as per given numbers 909/42, 969/65, 732/15 is
GCF of Numerators i.e. for 909,969,732 is 3
LCM of denominators i.e. for 42,65,15 is 2730.
Thus, GCF of Fractions is 3/2730.Finally, GCF of Fractions for 909/42, 969/65, 732/15 is 3/2730.