Can a composite number have composite and prime factors?

Answer 1

A composite number has more than two factors. A Prime number has exactly two factors.

A prime factor is a factor that is a prime number. All numbers can be written as a prime number or the product of prime factors. So, all composite numbers have prime factors. Here are examples:

10 = 2 x 5

11 = 11

12 = 2 x 2 x 3

13 = 13

14 = 2 x 7

15 = 3 x 5

16 = 2 x 2 x 2 x 2

Any number has itself as a factor, so all composite numbers have at least one composite factor - themselves. Some composite numbers have other composite numbers as factors, as well. If the composite number has only two (not necessarily distinct) prime factors, it will not have any other composite numbers as factors other than itself.

Here are examples:

20 has factors 1, 2, 4, 5, 10, and 20, of which 4, 10, and 20 are composite numbers.

21 has factors 1, 3, 7, and 21, of which only 21 is a composite number.

22 had factors 1, 2, 11, and 22, of which only 22 is a composite number.

24 has factors 1, 2, 3, 4, 6, 8, 12, and 24, of which 4, 6, 8, 12, and 24 are composite numbers.

A factor string of a composite number can be a combination of prime and composite factors that multiplied together equal the number. The prime factorization is a factor string with only the prime numbers.

Here are examples:

24 has a factor string of 4 x 6, both of which are composite numbers, or

3 x 8, of which one is a composite number and one is a prime number, or

2 x 3 x 4, of which one is a composite number and two are prime numbers, or

2 x 2 x 2 x 3, which is the prime factorization.

20 has a factor string of 4 x 5, of which one is a composite number and one is a prime number, or

2 x 2 x 5, which is the prime factorization.