Question

decide if each number below is a prime number composite number or neither (has less than 2 factors)
2 choose
4 choose
6 choose
1 choose
13 choose
27 choose
0 choose
49 choose
4 choose
7 choose

Explanation:

Step1: Define prime/composite/neither

A prime number has exactly 2 distinct positive factors (1 and itself). A composite number has 3+ distinct positive factors. Numbers with <2 factors are neither.

Step2: Evaluate 2

Factors: $1, 2$ → 2 factors.

Step3: Evaluate 4

Factors: $1, 2, 4$ → 3 factors.

Step4: Evaluate 6

Factors: $1, 2, 3, 6$ → 4 factors.

Step5: Evaluate 1

Factors: $1$ → 1 factor.

Step6: Evaluate 13

Factors: $1, 13$ → 2 factors.

Step7: Evaluate 27

Factors: $1, 3, 9, 27$ → 4 factors.

Step8: Evaluate 0

Has infinite factors, <2 valid positive factors.

Step9: Evaluate 49

Factors: $1, 7, 49$ → 3 factors.

Step10: Evaluate 4

Factors: $1, 2, 4$ → 3 factors.

Step11: Evaluate 7

Factors: $1, 7$ → 2 factors.

Answer:

2: Prime number
4: Composite number
6: Composite number
1: Neither
13: Prime number
27: Composite number
0: Neither
49: Composite number
4: Composite number
7: Prime number