Question

zoe created a factor table for the number 57.
select the three statements that are true.
factors of 57
1 57
3 19
57 has exactly two factors.
57 is a prime number.
57 is a composite number.
57 has more than two factors.
zoe’s factor table should not have the factor pair 3 and 19.
57 is an odd number.

Explanation:

To solve this, we analyze each statement using the factor table of 57 (factors: 1, 3, 19, 57) and number properties:

1. "57 has exactly two factors." → False. Prime numbers have exactly two factors (1 and themselves), but 57 has 1, 3, 19, 57 (four factors).
2. "57 is a prime number." → False. Prime numbers have only two factors; 57 has more (3 and 19 are also factors).
3. "57 is a composite number." → True. Composite numbers have more than two factors (57 has 1, 3, 19, 57).
4. "57 has more than two factors." → True. As shown, 57 has four factors (1, 3, 19, 57).
5. "Zoe’s factor table should not have the factor pair 3 and 19." → False. Since \( 3 \times 19 = 57 \), 3 and 19 are valid factors.
6. "57 is an odd number." → True. Odd numbers are not divisible by 2; 57 ÷ 2 = 28.5 (not an integer), so 57 is odd.

The three true statements are:

• 57 is a composite number.
• 57 has more than two factors.
• 57 is an odd number.

Answer:

• 57 is a composite number.
• 57 has more than two factors.
• 57 is an odd number.