How do you find prime factorization of a number?

Answer 1

Please see below.

To find prime factorization of a number, e have to first identify a prime number, which divides the given number. May times, it is easy if the number is divisible by #{2,3,5,7,11,13}# and one can use divisibility rule for this purpose. However if number is #n#, one need to try a prime number only till #sqrtn#. For details see this link.

Once a prime number has been found, divide the number by this, since it is a factor of the given number, and find the quotient. Next, try finding additional prime factors of the quotient, and so on, until you have found all the prime factors.

For example number #38115# is divisible by #9# (using divisibility test for #9#) and further it is also divisible by #5#, hence it will be divisible by #3xx3xx5# or #45#.
Dividing #38115# by #45#, we get #847#, which is divisible by #7# and dividing this number by #7# leads to #121#, whic is #11xx11#.
Hence prime factors of #38115# are given by #3xx3xx5xx7xx11xx11#.
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Answer 2

To find the prime factorization of a number:

  1. Start by dividing the number by the smallest prime number, 2.
  2. Continue dividing by primes until the quotient becomes 1.
  3. Write down each prime factor as you go.
  4. Repeat this process for the quotient until it equals 1.
  5. The prime factors you've written down represent the prime factorization of the original number.
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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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