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24 Feb 2021, 20:58
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Hello SME,
IF it is given a, b and C are Prime factors of number N. Can the the power of these factors be Zero.
N=( a^x).(b^y).(C^z)....
Can in the above prime factorization, x,y,z be zero.
Please advise.
Regards
IF it is given a, b and C are Prime factors of number N. Can the the power of these factors be Zero.
N=( a^x).(b^y).(C^z)....
Can in the above prime factorization, x,y,z be zero.
Please advise.
Regards
25 Feb 2021, 07:56
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No, it cannot
If A is a factor of N then A^x is a factor of N, where x is a positive integer greater than one
Posted from my mobile device
If A is a factor of N then A^x is a factor of N, where x is a positive integer greater than one
Posted from my mobile device
25 Feb 2021, 22:46
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vickytvn
We are glad that you ask questions!!
Coming to what you asked-Prime Factorization essentially implies writing a number as a product of its prime factors only.
If we say 25 can be written as 2^0 *5^2 (with 2^0=1)we are implying that 25 can be written as not only 2^0*5^2 but as a product of any prime number(s) like 3/7..etc(that are not present in the factorization of 25) raised to the power 0(3^0/7^0/etc) and multiplied with a 5^2 as well!! This would lead to an infinite representation.
A prime number not present in the prime factorization of the number is represented by a^0.
Thus, power of 0 is not used to represent the prime factorization of a number.
Hope you are clear on this now!
