Number Theory and Patterns

1. What is the greatest common divisor (GCD) of 12 and 18?

• A. 2
• B. 3
• C. 6 ✓
• D. 9

💡 The largest number that divides both 12 and 18 evenly is 6.

2. Is 91 a prime number?

• A. Yes
• B. No ✓
• C. Maybe
• D. Undefined

💡 91 is not prime, since it equals 7 x 13.

3. What is the next number in the pattern: 3, 6, 12, 24, __?

• A. 30
• B. 36
• C. 42
• D. 48 ✓

💡 Each number doubles the previous one, so the next number is 48.

4. How many factors does 12 have?

• A. 4
• B. 5
• C. 6 ✓
• D. 7

💡 12 has six factors: 1, 2, 3, 4, 6, and 12.

5. What is the least common multiple (LCM) of 4 and 6?

• A. 8
• B. 10
• C. 12 ✓
• D. 14

💡 The smallest number divisible by both 4 and 6 is 12.

6. What is the cube root of 27?

• A. 2
• B. 3 ✓
• C. 4
• D. 5

💡 3 x 3 x 3 = 27, so the cube root of 27 is 3.

7. Is 0 an even number?

• A. Yes ✓
• B. No
• C. Sometimes
• D. Undefined

💡 0 is considered an even number since it is divisible by 2.

8. What is the next number in the Fibonacci sequence: 1, 1, 2, 3, 5, __?

• A. 6
• B. 7
• C. 8 ✓
• D. 9

💡 Each Fibonacci number is the sum of the two before it: 3 + 5 = 8.

9. What is the remainder when 17 is divided by 5?

• A. 1
• B. 2 ✓
• C. 3
• D. 4

💡 17 divided by 5 is 3 with a remainder of 2.

10. What is 2^5 (2 to the power of 5)?

• A. 16
• B. 25
• C. 32 ✓
• D. 64

💡 2 x 2 x 2 x 2 x 2 = 32.

11. What is the square of 12?

• A. 122
• B. 124
• C. 144 ✓
• D. 146

💡 12 squared (12 x 12) equals 144.

12. What is the absolute value of -15?

• A. -15
• C. 15 ✓
• D. 30

💡 The absolute value of -15 is 15, its distance from zero.

13. What is the sum of the digits of 12345?

• A. 12
• B. 14
• C. 15 ✓
• D. 16

💡 1 + 2 + 3 + 4 + 5 = 15.

14. What is the next prime number after 7?

• A. 8
• B. 9
• C. 10
• D. 11 ✓

💡 11 is the next prime number after 7, since 8, 9, and 10 are all composite.

15. What is the sum of the first 5 even numbers?

• A. 20
• B. 25
• C. 30 ✓
• D. 35

💡 2 + 4 + 6 + 8 + 10 = 30.