GCF of 226/16, 294/72, 765/48
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 226/16, 294/72, 765/48 i.e 1/144 easily. The following is the detailed procedure to determine the greatest common factor of fractions 226/16, 294/72, 765/48.
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 226/16,294/72,765/48?
Given fractions are 226/16,294/72,765/48
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 226/16,294/72,765/48, numerators are 226,294,765
Denominators are 16,72,48
The GCF of 226,294,765 is 1 .
LCM of 16,72,48 is 144.
The greatest common factor of 226/16,294/72,765/48 = [GCF of 226,294,765]/[LCM of 16,72,48]= 1/144
Therefore, the GCF of 226/16,294/72,765/48 is 1/144.
To find the highest common factor of 226,294,765, we have to find the factors of both numbers and list the highest common factor.
The factors of 226 are 1, 2, 113, 226
The factors of 294 are 1, 2, 3, 6, 7, 14, 21, 42, 49, 98, 147, 294
The factors of 765 are 1, 3, 5, 9, 15, 17, 45, 51, 85, 153, 255, 765
The HCF of 226,294,765 is 1.
Lets's calculate GCF of 226,294,765
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 226,294,765 By Matching Biggest Common Factor Method
Now, list down the factors of 226
:1,2,113,226
Now, list down the factors of 294
:1,2,3,6,7,14,21,42,49,98,147,294
Now, list down the factors of 765
:1,3,5,9,15,17,45,51,85,153,255,765
Greatest Common Factor
We found the factors 226,294,765 . The biggest common factor number is the GCF number.
So the greatest common factor 226,294,765 is 1.
Lets's calculate LCM of 16,72,48
| 2 | 16, 72, 48 |
| 2 | 8, 36, 24 |
| 2 | 4, 18, 12 |
| 2 | 2, 9, 6 |
| 3 | 1, 9, 3 |
| 1, 1, 3 |
∴ So the LCM of the given numbers is 2 x 2 x 2 x 2 x 3 x 1 x 1 x 3 = 144
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/144
Therefore, the GCF of Fractions 226/16,294/72,765/48 is 1/144
Least Common Multiple of 16,72,48 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 16,72,48 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(16,72,48) = 8
common factors(in case of two or more numbers have common factors) = 48
GCF(16,72,48) x common factors =8 x 48 = 384
LCM(16,72,48) = ( 16 × 72 × 48 ) / 384
LCM(16,72,48) = 55296 / 384
LCM(16,72,48) = 144
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FAQs on GCF of Fractions of 226/16, 294/72, 765/48
1. What is the HCF of 226,294,765?
The HCF of 226,294,765 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 226/16, 294/72, 765/48?
Answer: GCF of Numerators as per given numbers 226/16, 294/72, 765/48 is
GCF of Numerators i.e. for 226,294,765 is 1
LCM of denominators i.e. for 16,72,48 is 144.
Thus, GCF of Fractions is 1/144.Finally, GCF of Fractions for 226/16, 294/72, 765/48 is 1/144.