Question

Is 181 prime or composite? Justify your answer. A. 181 is prime because it has a factor of 9. B. 181 is prime because its only factors are 1 and itself. C. 181 is composite because it has a factor of 9. D. 181 is composite because it has a factor of 3.

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Answer 1

B

Explanation:

Assuming these 4 are the only possibilities:

A: This cannot be correct because if 181 were divisible by 9, it would not be prime, as the problem suggests.

C: This cannot be correct because 181/9 is 21.11, which is not a whole number

D: This cannot be correct because 181/3 is 60.333, which is not a whole number

Thus, the answer is B.

FUN FACT:

When seeing whether a number is divisible by 3, add up its digits, and if they are divisible by 3, so is the number. Example: 36 is divisible by 3 because 3 + 6 = 9, and 9 is divisible by 3. 181 is not, however, because 1+8+1=10, and 10 is not divisible by 3.

Same with 9! 459 is divisible by 9 because 4+5+9 = 18, which is divisible by 9. 181 is not, however, because 1+8+1 = 10, which is not divisible by 9.

I hope this helps!

Answer 2

B. 181 is prime because its only factors are 1 and itself.

Explanation:

Prime number

A whole number greater than 1 that cannot be made by multiplying other whole numbers (its only factors are 1 and itself).

Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, etc.

Composite number

A number that is divisible by a number other than 1 and itself (so it has more than 2 factors).

An example of a composite number is 6 as its factors are 1, 2, 3 and 6.

The factors of 181 are 1 and 181.

Therefore, it is prime because its only factors are 1 and itself.