Question

which number is prime? 28 51 39 29

Explanation:

Step1: Recall prime number definition

A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.

Step2: Analyze 28

Factorize 28: \(28 = 2\times14 = 2\times2\times7\). So, 28 has divisors other than 1 and itself (e.g., 2, 4, 7, 14), so not prime.

Step3: Analyze 51

Factorize 51: \(51 = 3\times17\). Divisors 3 and 17 exist, so not prime.

Step4: Analyze 39

Factorize 39: \(39 = 3\times13\). Divisors 3 and 13 exist, so not prime.

Step5: Analyze 29

Check divisors of 29. Numbers less than \(\sqrt{29}\approx5.38\) are 2, 3, 4, 5. 29 is not divisible by 2 (29 is odd), not divisible by 3 (\(3\times9 = 27\), \(3\times10 = 30\)), not divisible by 4 or 5. So 29's only divisors are 1 and 29, so it is prime.

Answer:

29 (the number in the bottom - right box)