Roster form using factors

Correct answer: A. Positive factors of 6

The governing concept is distinguishing factors from multiples. A positive factor of 6 is a positive whole number that divides 6 exactly, leaving remainder zero. The divisions 6 ÷ 1 = 6, 6 ÷ 2 = 3, 6 ÷ 3 = 2, and 6 ÷ 6 = 1 show that 1, 2, 3, and 6 are precisely the positive factors of 6. Therefore option A is correct. Multiples of 6 would include 6, 12, 18, and so on, so option B does not match. Even numbers less than 6 are 2 and 4, while odd numbers less than 6 are 1, 3, and 5. Neither option C nor D gives exactly the listed set.

Correct answer: A. A = {1, 2, 4, 8, 16}

The governing concept is writing a set in roster form by listing every positive factor that divides 16 exactly. Testing the divisors gives 16 ÷ 1 = 16, 16 ÷ 2 = 8, 16 ÷ 4 = 4, 16 ÷ 8 = 2, and 16 ÷ 16 = 1, all with no remainder. Thus the complete set of positive factors is {1, 2, 4, 8, 16}. Option B contains numbers such as 6, 10, 12, and 14 that do not divide 16 exactly. Option C lists multiples of 16 rather than factors, and option D omits 2 and 8. Therefore option A lists all and only the required factors.