The prime factorization of 2024 is 2 x 2 x 2 x 3 x 7 x 11 or, expressed using exponents, 23 x 31 x 71.
To find the prime factorization, we start by dividing 2024 by the smallest prime number, which is 2. When we divide, we find:
- 2024 ÷ 2 = 1012
- 1012 ÷ 2 = 506
- 506 ÷ 2 = 253
At this point, 253 is no longer divisible by 2, so we move to the next smallest prime number, which is 3. However, 253 is not divisible by 3. The next prime number is 5, and it’s also not divisible. Finally, we check 7:
- 253 ÷ 7 = 36.14 (not an integer)
Next, we try 11:
- 253 ÷ 11 = 23
Since 23 is also a prime number, our factorization is complete. The complete prime factorization can be expressed as:
23 x 71 x 111
Thus, the prime factors of 2024 are 2, 3, 7, and 11.