GCF of 15/32, 102/70, 243/460
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 15/32, 102/70, 243/460 i.e 3/25760 easily. The following is the detailed procedure to determine the greatest common factor of fractions 15/32, 102/70, 243/460.
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 15/32,102/70,243/460?
Given fractions are 15/32,102/70,243/460
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 15/32,102/70,243/460, numerators are 15,102,243
Denominators are 32,70,460
The GCF of 15,102,243 is 3 .
LCM of 32,70,460 is 25760.
The greatest common factor of 15/32,102/70,243/460 = [GCF of 15,102,243]/[LCM of 32,70,460]= 3/25760
Therefore, the GCF of 15/32,102/70,243/460 is 3/25760.
To find the highest common factor of 15,102,243, we have to find the factors of both numbers and list the highest common factor.
The factors of 15 are 1, 3, 5, 15
The factors of 102 are 1, 2, 3, 6, 17, 34, 51, 102
The factors of 243 are 1, 3, 9, 27, 81, 243
The HCF of 15,102,243 is 3.
Lets's calculate GCF of 15,102,243
| 3 | 15, 102, 243 |
| 5, 34, 81 |
∴ So the GCF of the given numbers is 3 = 3
Greatest Common Factor of 15,102,243 By Matching Biggest Common Factor Method
Now, list down the factors of 15
:1,3,5,15
Now, list down the factors of 102
:1,2,3,6,17,34,51,102
Now, list down the factors of 243
:1,3,9,27,81,243
Greatest Common Factor
We found the factors 15,102,243 . The biggest common factor number is the GCF number.
So the greatest common factor 15,102,243 is 3.
Lets's calculate LCM of 32,70,460
| 2 | 32, 70, 460 |
| 2 | 16, 35, 230 |
| 5 | 8, 35, 115 |
| 8, 7, 23 |
∴ So the LCM of the given numbers is 2 x 2 x 5 x 8 x 7 x 23 = 25760
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 3/25760
Therefore, the GCF of Fractions 15/32,102/70,243/460 is 3/25760
Least Common Multiple of 32,70,460 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 32,70,460 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(32,70,460) = 2
common factors(in case of two or more numbers have common factors) = 20
GCF(32,70,460) x common factors =2 x 20 = 40
LCM(32,70,460) = ( 32 × 70 × 460 ) / 40
LCM(32,70,460) = 1030400 / 40
LCM(32,70,460) = 25760
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FAQs on GCF of Fractions of 15/32, 102/70, 243/460
1. What is the HCF of 15,102,243?
The HCF of 15,102,243 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 15/32, 102/70, 243/460?
Answer: GCF of Numerators as per given numbers 15/32, 102/70, 243/460 is
GCF of Numerators i.e. for 15,102,243 is 3
LCM of denominators i.e. for 32,70,460 is 25760.
Thus, GCF of Fractions is 3/25760.Finally, GCF of Fractions for 15/32, 102/70, 243/460 is 3/25760.