Answers – Prime Numbers – 2

Answer: Yes, 53 is a prime number.

Working:

To determine if 53 is prime, I need to check if it has any factors other than 1 and 53.

• I only need to check divisibility by numbers up to √53 ≈ 7.28
• So I’ll check if 53 is divisible by 2, 3, 5, 7

53 ÷ 2 = 26.5 (not divisible by 2)
53 ÷ 3 = 17.67… (not divisible by 3)
53 ÷ 5 = 10.6 (not divisible by 5)
53 ÷ 7 = 7.57… (not divisible by 7)

Since 53 is not divisible by any prime number less than or equal to its square root, 53 is a prime number.

Answer: No, 121 is not a prime number.

Working:

To determine if 121 is prime, I need to check if it has any factors other than 1 and 121.

• I only need to check divisibility by numbers up to √121 = 11
• So I’ll check if 121 is divisible by 2, 3, 5, 7, 11

121 ÷ 2 = 60.5 (not divisible by 2)
121 ÷ 3 = 40.33… (not divisible by 3)
121 ÷ 5 = 24.2 (not divisible by 5)
121 ÷ 7 = 17.28… (not divisible by 7)
121 ÷ 11 = 11 (divisible by 11)

Since 121 = 11 × 11 = 11², it has factors other than 1 and itself.
Therefore, 121 is not a prime number.

Answer: Yes, 89 is a prime number.

Working:

To determine if 89 is prime, I need to check if it has any factors other than 1 and 89.

• I only need to check divisibility by numbers up to √89 ≈ 9.43
• So I’ll check if 89 is divisible by 2, 3, 5, 7

89 ÷ 2 = 44.5 (not divisible by 2)
89 ÷ 3 = 29.67… (not divisible by 3)
89 ÷ 5 = 17.8 (not divisible by 5)
89 ÷ 7 = 12.71… (not divisible by 7)

Since 89 is not divisible by any prime number less than or equal to its square root, 89 is a prime number.

Answer: No, 143 is not a prime number.

Working:

To determine if 143 is prime, I need to check if it has any factors other than 1 and 143.

• I only need to check divisibility by numbers up to √143 ≈ 11.96
• So I’ll check if 143 is divisible by 2, 3, 5, 7, 11

143 ÷ 2 = 71.5 (not divisible by 2)
143 ÷ 3 = 47.67… (not divisible by 3)
143 ÷ 5 = 28.6 (not divisible by 5)
143 ÷ 7 = 20.42… (not divisible by 7)
143 ÷ 11 = 13 (divisible by 11)

Since 143 = 11 × 13, it has factors other than 1 and itself.
Therefore, 143 is not a prime number.

Answer: Yes, 211 is a prime number.

Working:

To determine if 211 is prime, I need to check if it has any factors other than 1 and 211.

• I only need to check divisibility by numbers up to √211 ≈ 14.53
• So I’ll check if 211 is divisible by 2, 3, 5, 7, 11, 13

211 ÷ 2 = 105.5 (not divisible by 2)
211 ÷ 3 = 70.33… (not divisible by 3)
211 ÷ 5 = 42.2 (not divisible by 5)
211 ÷ 7 = 30.14… (not divisible by 7)
211 ÷ 11 = 19.18… (not divisible by 11)
211 ÷ 13 = 16.23… (not divisible by 13)

Since 211 is not divisible by any prime number less than or equal to its square root, 211 is a prime number.

Answer: No, 57 is not a prime number.

Working:

To determine if 57 is prime, I need to check if it has any factors other than 1 and 57.

• I only need to check divisibility by numbers up to √57 ≈ 7.55
• So I’ll check if 57 is divisible by 2, 3, 5, 7

57 ÷ 2 = 28.5 (not divisible by 2)
57 ÷ 3 = 19 (divisible by 3)

Since 57 = 3 × 19, it has factors other than 1 and itself.
Therefore, 57 is not a prime number.

Answer: Yes, 173 is a prime number.

Working:

To determine if 173 is prime, I need to check if it has any factors other than 1 and 173.

• I only need to check divisibility by numbers up to √173 ≈ 13.15
• So I’ll check if 173 is divisible by 2, 3, 5, 7, 11, 13

173 ÷ 2 = 86.5 (not divisible by 2)
173 ÷ 3 = 57.67… (not divisible by 3)
173 ÷ 5 = 34.6 (not divisible by 5)
173 ÷ 7 = 24.71… (not divisible by 7)
173 ÷ 11 = 15.73… (not divisible by 11)
173 ÷ 13 = 13.31… (not divisible by 13)

Since 173 is not divisible by any prime number less than or equal to its square root, 173 is a prime number.

Answer: No, 221 is not a prime number.

Working:

To determine if 221 is prime, I need to check if it has any factors other than 1 and 221.

• I only need to check divisibility by numbers up to √221 ≈ 14.87
• So I’ll check if 221 is divisible by 2, 3, 5, 7, 11, 13

221 ÷ 2 = 110.5 (not divisible by 2)
221 ÷ 3 = 73.67… (not divisible by 3)
221 ÷ 5 = 44.2 (not divisible by 5)
221 ÷ 7 = 31.57… (not divisible by 7)
221 ÷ 11 = 20.09… (not divisible by 11)
221 ÷ 13 = 17 (divisible by 13)

Since 221 = 13 × 17, it has factors other than 1 and itself.
Therefore, 221 is not a prime number.

Answer: Yes, 101 is a prime number.

Working:

To determine if 101 is prime, I need to check if it has any factors other than 1 and 101.

• I only need to check divisibility by numbers up to √101 ≈ 10.05
• So I’ll check if 101 is divisible by 2, 3, 5, 7

101 ÷ 2 = 50.5 (not divisible by 2)
101 ÷ 3 = 33.67… (not divisible by 3)
101 ÷ 5 = 20.2 (not divisible by 5)
101 ÷ 7 = 14.43… (not divisible by 7)

Since 101 is not divisible by any prime number less than or equal to its square root, 101 is a prime number.

Answer: No, 289 is not a prime number.

Working:

To determine if 289 is prime, I need to check if it has any factors other than 1 and 289.

• I only need to check divisibility by numbers up to √289 = 17
• So I’ll check if 289 is divisible by 2, 3, 5, 7, 11, 13, 17

289 ÷ 2 = 144.5 (not divisible by 2)
289 ÷ 3 = 96.33… (not divisible by 3)
289 ÷ 5 = 57.8 (not divisible by 5)
289 ÷ 7 = 41.29… (not divisible by 7)
289 ÷ 11 = 26.27… (not divisible by 11)
289 ÷ 13 = 22.23… (not divisible by 13)
289 ÷ 17 = 17 (divisible by 17)

Since 289 = 17 × 17 = 17², it has factors other than 1 and itself.
Therefore, 289 is not a prime number.