What does a factorization look like?

Answer 1

The prime factorization of a number uses only primes.

Ex: The prime factorization of 12 is not 6 x 2, and not 4 x 3, because 6 and 4 are not prime numbers. The prime factorization is 2 x 2 x 3. Their product is 12 and all factors are prime numbers.

To get a prime factorization you are usually taught to factor through division by small prime numbers, sometimes you must use the same number more than once as in the example of 12 above 2 was used twice.

Ex: find the prime factorization of 18.

The smallest prime is 2... divide by 2

18 / 2 = 9 .... for the next step divide 9 by a prime

9 / 3 = 3 ... this is a prme ... it is also a factor

so the prime factorization is 18 = 2x3x3

Ex. find the prime factorization of 35.

35 cannot be divided by 2, or 3, so use 5 first

35 / 5 = 7 .... since 7 is a prime we are finished.

The prime factorization of 35 is

35 = 5 x 7

Some teachers teach this using a "factor tree" .. I can't type one of those on a computer.

Answer 2

It looks like a whole number.