Which number between 29 and 39 has three different prime factors?What is the prime factorization of this number?

11 o 3 o 2

30: 2*3*5

30

To find the number between 29 and 39 that has three different prime factors, we need to check the prime factorization of each number and count the number of distinct prime factors.

Prime factorization means breaking down a number into its prime factors, which are the prime numbers that multiply together to form that number. For example, the prime factorization of 18 is 2 * 3 * 3 since 2, 3, and 3 are prime factors that multiply to give 18.

Let's check the prime factorization of the numbers between 29 and 39:

29: Since 29 is a prime number itself, its prime factorization is simply 29.

30: We can divide 30 by the smallest prime number, 2, which results in 15. Then we can divide 15 by 3 to get 5. So the prime factorization of 30 is 2 * 3 * 5.

31: 31 is also a prime number, so its prime factorization is just 31.

32: 32 can be divided by 2 repeatedly until we reach 1. So the prime factorization of 32 is 2 * 2 * 2 * 2 * 2, which can be written as 2^5.

33: 33 can be divided by 3 and results in 11. Therefore, the prime factorization of 33 is 3 * 11.

34: 34 can be divided by 2 to get 17. So the prime factorization of 34 is 2 * 17.

35: 35 can be divided by 5 and results in 7. Therefore, the prime factorization of 35 is 5 * 7.

36: 36 can be divided by 2 repeatedly, resulting in 2 * 2 * 3 * 3. So the prime factorization of 36 is 2^2 * 3^2.

37: 37 is a prime number, so its prime factorization is 37.

38: 38 can be divided by 2 to get 19. So the prime factorization of 38 is 2 * 19.

39: 39 can be divided by 3 and results in 13. Therefore, the prime factorization of 39 is 3 * 13.

Now, let's analyze the prime factorizations. The numbers between 29 and 39 that have three different prime factors are 30 (2 * 3 * 5), 36 (2^2 * 3^2), and 38 (2 * 19).

Therefore, the number between 29 and 39 that has three different prime factors is 38, and its prime factorization is 2 * 19.