GCF of 23/157, 414/438, 460/223
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 23/157, 414/438, 460/223 i.e 23/15334818 easily. The following is the detailed procedure to determine the greatest common factor of fractions 23/157, 414/438, 460/223.
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 23/157,414/438,460/223?
Given fractions are 23/157,414/438,460/223
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 23/157,414/438,460/223, numerators are 23,414,460
Denominators are 157,438,223
The GCF of 23,414,460 is 23 .
LCM of 157,438,223 is 15334818.
The greatest common factor of 23/157,414/438,460/223 = [GCF of 23,414,460]/[LCM of 157,438,223]= 23/15334818
Therefore, the GCF of 23/157,414/438,460/223 is 23/15334818.
To find the highest common factor of 23,414,460, we have to find the factors of both numbers and list the highest common factor.
The factors of 23 are 1, 23
The factors of 414 are 1, 2, 3, 6, 9, 18, 23, 46, 69, 138, 207, 414
The factors of 460 are 1, 2, 4, 5, 10, 20, 23, 46, 92, 115, 230, 460
The HCF of 23,414,460 is 23.
Lets's calculate GCF of 23,414,460
| 23 | 23, 414, 460 |
| 1, 18, 20 |
∴ So the GCF of the given numbers is 23 = 23
Greatest Common Factor of 23,414,460 By Matching Biggest Common Factor Method
Now, list down the factors of 23
:1,23
Now, list down the factors of 414
:1,2,3,6,9,18,23,46,69,138,207,414
Now, list down the factors of 460
:1,2,4,5,10,20,23,46,92,115,230,460
Greatest Common Factor
We found the factors 23,414,460 . The biggest common factor number is the GCF number.
So the greatest common factor 23,414,460 is 23.
Lets's calculate LCM of 157,438,223
Given numbers has no common factors except 1. So, there LCM is their product i.e 15334818
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 23/15334818
Therefore, the GCF of Fractions 23/157,414/438,460/223 is 23/15334818
Least Common Multiple of 157,438,223 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 157,438,223 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(157,438,223) = 1
common factors(in case of two or more numbers have common factors) = 1
GCF(157,438,223) x common factors =1 x 1 = 1
LCM(157,438,223) = ( 157 × 438 × 223 ) / 1
LCM(157,438,223) = 15334818 / 1
LCM(157,438,223) = 15334818
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FAQs on GCF of Fractions of 23/157, 414/438, 460/223
1. What is the HCF of 23,414,460?
The HCF of 23,414,460 is 23
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 23/157, 414/438, 460/223?
Answer: GCF of Numerators as per given numbers 23/157, 414/438, 460/223 is
GCF of Numerators i.e. for 23,414,460 is 23
LCM of denominators i.e. for 157,438,223 is 15334818.
Thus, GCF of Fractions is 23/15334818.Finally, GCF of Fractions for 23/157, 414/438, 460/223 is 23/15334818.