GCF of 324/414, 157/404
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 324/414, 157/404 i.e 1/83628 easily. The following is the detailed procedure to determine the greatest common factor of fractions 324/414, 157/404.
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 324/414,157/404?
Given fractions are 324/414,157/404
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 324/414,157/404, numerators are 324,157
Denominators are 414,404
The GCF of 324,157 is 1 .
LCM of 414,404 is 83628.
The greatest common factor of 324/414,157/404 = [GCF of 324,157]/[LCM of 414,404]= 1/83628
Therefore, the GCF of 324/414,157/404 is 1/83628.
To find the highest common factor of 324,157, we have to find the factors of both numbers and list the highest common factor.
The factors of 324 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108, 162, 324
The factors of 157 are 1, 157
The HCF of 324,157 is 1.
Lets's calculate GCF of 324,157
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 324,157 By Matching Biggest Common Factor Method
Now, list down the factors of 324
:1,2,3,4,6,9,12,18,27,36,54,81,108,162,324
Now, list down the factors of 157
:1,157
Greatest Common Factor
We found the factors 324,157 . The biggest common factor number is the GCF number.
So the greatest common factor 324,157 is 1.
Lets's calculate LCM of 414,404
| 2 | 414, 404 |
| 207, 202 |
∴ So the LCM of the given numbers is 2 x 207 x 202 = 83628
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/83628
Therefore, the GCF of Fractions 324/414,157/404 is 1/83628
Least Common Multiple of 414,404 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 414,404 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(414,404) = 2
common factors(in case of two or more numbers have common factors) = 1
GCF(414,404) x common factors =2 x 1 = 2
LCM(414,404) = ( 414 × 404 ) / 2
LCM(414,404) = 167256 / 2
LCM(414,404) = 83628
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FAQs on GCF of Fractions of 324/414, 157/404
1. What is the HCF of 324,157?
The HCF of 324,157 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 324/414, 157/404?
Answer: GCF of Numerators as per given numbers 324/414, 157/404 is
GCF of Numerators i.e. for 324,157 is 1
LCM of denominators i.e. for 414,404 is 83628.
Thus, GCF of Fractions is 1/83628.Finally, GCF of Fractions for 324/414, 157/404 is 1/83628.