Which number between 20 and 29 has 2 and 3 in its prime factorization?
24
To find the number between 20 and 29 that has 2 and 3 in its prime factorization, we can divide each number in this range by 2 and 3, respectively, and check if the resulting quotient is a whole number.
Let's start by checking the prime factorization of each number:
- For the number 20: The prime factorization of 20 is 2 * 2 * 5. It contains 2 but not 3.
- For the number 21: The prime factorization of 21 is 3 * 7. It contains 3 but not 2.
- For the number 22: The prime factorization of 22 is 2 * 11. It contains 2 but not 3.
- For the number 23: The prime factorization of 23 is 23. It does not contain 2 or 3.
- For the number 24: The prime factorization of 24 is 2 * 2 * 2 * 3. It contains both 2 and 3.
- For the number 25: The prime factorization of 25 is 5 * 5. It does not contain 2 or 3.
- For the number 26: The prime factorization of 26 is 2 * 13. It contains 2 but not 3.
- For the number 27: The prime factorization of 27 is 3 * 3 * 3. It contains both 2 and 3.
- For the number 28: The prime factorization of 28 is 2 * 2 * 7. It contains 2 but not 3.
- For the number 29: The prime factorization of 29 is 29. It does not contain 2 or 3.
From the numbers in the range 20 to 29, the only numbers that have both 2 and 3 in their prime factorization are 24 and 27.