Answers – Prime Numbers – 1

Answer: Yes, 37 is a prime number.

Working:

A prime number is a natural number greater than 1 that is not divisible by any positive integer other than 1 and itself.

To determine if 37 is prime, I need to check if it has any factors other than 1 and 37.

• I only need to check divisibility by numbers up to √37 ≈ 6.08
• So I’ll check if 37 is divisible by 2, 3, 5, or 6

37 ÷ 2 = 18.5 (not divisible by 2)
37 ÷ 3 = 12.33… (not divisible by 3)
37 ÷ 5 = 7.4 (not divisible by 5)

Since 37 is not divisible by any prime number less than or equal to its square root, 37 is a prime number.

Answer: No, 91 is not a prime number.

Working:

To determine if 91 is prime, I need to check if it has any factors other than 1 and 91.

• I only need to check divisibility by numbers up to √91 ≈ 9.54
• So I’ll check if 91 is divisible by 2, 3, 5, 7

91 ÷ 2 = 45.5 (not divisible by 2)
91 ÷ 3 = 30.33… (not divisible by 3)
91 ÷ 5 = 18.2 (not divisible by 5)
91 ÷ 7 = 13 (divisible by 7)

Since 91 = 7 × 13, it has factors other than 1 and itself.
Therefore, 91 is not a prime number.

Answer: Yes, 127 is a prime number.

Working:

To determine if 127 is prime, I need to check if it has any factors other than 1 and 127.

• I only need to check divisibility by numbers up to √127 ≈ 11.27
• So I’ll check if 127 is divisible by 2, 3, 5, 7, 11

127 ÷ 2 = 63.5 (not divisible by 2)
127 ÷ 3 = 42.33… (not divisible by 3)
127 ÷ 5 = 25.4 (not divisible by 5)
127 ÷ 7 = 18.14… (not divisible by 7)
127 ÷ 11 = 11.54… (not divisible by 11)

Since 127 is not divisible by any prime number less than or equal to its square root, 127 is a prime number.

Answer: No, 169 is not a prime number.

Working:

To determine if 169 is prime, I need to check if it has any factors other than 1 and 169.

• I only need to check divisibility by numbers up to √169 = 13
• So I’ll check if 169 is divisible by 2, 3, 5, 7, 11, 13

169 ÷ 2 = 84.5 (not divisible by 2)
169 ÷ 3 = 56.33… (not divisible by 3)
169 ÷ 5 = 33.8 (not divisible by 5)
169 ÷ 7 = 24.14… (not divisible by 7)
169 ÷ 11 = 15.36… (not divisible by 11)
169 ÷ 13 = 13 (divisible by 13)

Since 169 = 13 × 13 = 13², it has factors other than 1 and itself.
Therefore, 169 is not a prime number.

Answer: No, 187 is not a prime number.

Working:

To determine if 187 is prime, I need to check if it has any factors other than 1 and 187.

• I only need to check divisibility by numbers up to √187 ≈ 13.67
• So I’ll check if 187 is divisible by 2, 3, 5, 7, 11, 13

187 ÷ 2 = 93.5 (not divisible by 2)
187 ÷ 3 = 62.33… (not divisible by 3)
187 ÷ 5 = 37.4 (not divisible by 5)
187 ÷ 7 = 26.71… (not divisible by 7)
187 ÷ 11 = 17 (divisible by 11)

Since 187 = 11 × 17, it has factors other than 1 and itself.
Therefore, 187 is not a prime number.