How many composite numbers lie between 31 and 37?

• A. 4
• B. 5
• C. 6
• D. 3

Answer: (B)

To determine the number of composite numbers between 31 and 37, we first need to identify what composite numbers are. A composite number is a positive integer that has at least one positive divisor other than one and itself, meaning it can be divided by numbers other than just 1 and itself.

The integers between 31 and 37 are 32, 33, 34, 35, and 36.

• 32: This number is composite because it can be divided by 1, 2, 4, 8, 16, and 32.

• 33: This number is also composite since it can be divided by 1, 3, 11, and 33.

• 34: This number is composite as well because it can be divided by 1, 2, 17, and 34.

• 35: This number is composite; it can be divided by 1, 5, 7, and 35.

• 36: This number is composite since it can be divided by 1, 2, 3, 4, 6, 9, 12, 18, and 36.

All five of these numbers—