Which one of the following is true about all the factors of 28?a) 1, 2, 14, 28b) 1, 2, 3, 4, 7, 14, 28c) 1, 3, 5, 7, 9, 11, 28d) 1, 2, 4, 7, 14, 28

To determine which option correctly lists all the factors of 28, let's first identify the factors of 28.

Break Down the Problem

1. Identify the factors of the number 28.
2. Compare the factors found with the options provided to see which one is accurate.

Relevant Concepts

• Factors are the numbers that divide another number exactly without leaving a remainder.

Analysis and Detail

1. Start by finding the prime factorization of 28: $28 = 2^2 \times 7^1$

2. To find all factors, we can multiply the factors of the prime factorization:

   • The possible combinations of the prime factors are:
     • $1$ (i.e., $2^0 \times 7^0$)
     • $2$ (i.e., $2^1 \times 7^0$)
     • $4$ (i.e., $2^2 \times 7^0$)
     • $7$ (i.e., $2^0 \times 7^1$)
     • $14$ (i.e., $2^1 \times 7^1$)
     • $28$ (i.e., $2^2 \times 7^1$)

3. Listing these, the complete set of factors of 28 is: $1, 2, 4, 7, 14, 28$

Verify and Summarize

Now, let's compare these factors to the options provided:

• a) $1, 2, 14, 28$ - Incomplete (missing 4 and 7).
• b) $1, 2, 3, 4, 7, 14, 28$ - Incorrect (contains 3, which is not a factor).
• c) $1, 3, 5, 7, 9, 11, 28$ - Incorrect (contains 3, 5, 9, and 11 which are not factors).
• d) $1, 2, 4, 7, 14, 28$ - Correct (includes all factors).

Final Answer

The correct answer is: d) 1, 2, 4, 7, 14, 28.