To determine the prime factorization of the numbers 24, 36, and 43, we will break each number down into its prime factors.
1. Prime Factorization of 24:
- Step 1: Start with the smallest prime number, which is 2.
- 24 is divisible by 2 (24 ÷ 2 = 12). So, 2 is a factor.
- 12 is divisible by 2 (12 ÷ 2 = 6). So, 2 is a factor again.
- 6 is divisible by 2 (6 ÷ 2 = 3). So, 2 is a factor again.
- Now, we have 3 left, which is a prime number.
Therefore, the prime factorization of 24 is:
[tex]\( 24 = 2 \times 2 \times 2 \times 3 \)[/tex]
or, using exponents,
[tex]\( 24 = 2^3 \times 3 \)[/tex].
2. Prime Factorization of 36:
- Step 1: Start with the smallest prime number, which is 2.
- 36 is divisible by 2 (36 ÷ 2 = 18). So, 2 is a factor.
- 18 is divisible by 2 (18 ÷ 2 = 9). So, 2 is a factor again.
- Now, we have 9 left, which is not divisible by 2. Move to the next smallest prime number, which is 3.
- 9 is divisible by 3 (9 ÷ 3 = 3). So, 3 is a factor.
- 3 is divisible by 3 (3 ÷ 3 = 1). So, 3 is a factor again.
Therefore, the prime factorization of 36 is:
[tex]\( 36 = 2 \times 2 \times 3 \times 3 \)[/tex]
or, using exponents,
[tex]\( 36 = 2^2 \times 3^2 \)[/tex].
3. Prime Factorization of 43:
- 43 is a prime number, so it is not divisible by any number other than 1 and itself.
Therefore, the prime factorization of 43 is simply:
[tex]\( 43 = 43 \)[/tex].
Summarizing the prime factorizations:
- [tex]\( 24 = 2^3 \times 3 \)[/tex]
- [tex]\( 36 = 2^2 \times 3^2 \)[/tex]
- [tex]\( 43 = 43 \)[/tex]
So, the results are:
- [tex]\( 24 \)[/tex] is factorized into [tex]\([2, 2, 2, 3]\)[/tex]
- [tex]\( 36 \)[/tex] is factorized into [tex]\([2, 2, 3, 3]\)[/tex]
- [tex]\( 43 \)[/tex] is factorized into [tex]\([43]\)[/tex]
