Are "prime factorization" and "integer factorization" the same?

Question

Are "prime factorization" and "integer factorization" the same? If not, what is the difference?

Answer 1

The expressions: prime factorization, integer factorization, and prime decomposition are common "short forms" of saying "factorization of an integer into primes". (Indeed, if you search Wikipedia for "prime factorization" or "prime decomposition", both phrases "redirect" to the entry entitled "integer factorization".) We can always factor/decompose an integer $n>1$ into its prime factors: this can always be done, and it can be done uniquely. See the Fundamental Theorem of Arithmetic.

For a clearer understanding about integer factors, divisors, and factorization of an integer into primes, see these Khan Academy video tutorials.

Answer 2

Prime factorization is factors in the form of prime numbers e.g. 24 = 2 × 2 × 2 × 3 here only prime numbers are there in the factors in integer factorization factors need not be prime factors

e.g 24 = 2 × 12 or 3 × 8 or 4 × 6