Challenge Exercises for Number Theory

Directions: Read each question below. Click once in an ANSWER BOX and type in your answer; then click ENTER. Do not enter commas in your answers. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.

1. One rectangular rug has an area of 24 square yards. Another rectangular rug has an area of 90 square yards. If you examine all whole-number dimensions each rug can have, what is the largest possible dimension common to both rugs?

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2. A school hallway has a long row of lockers. Every sixth locker contains a package of chewing gum, every eighth locker contains a mirror, and every ninth locker contains a hockey stick. What is the first locker that contains all three items?

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3. Name one prime number from 70 and 79.

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4. The number 279 is composite. Name a number other than 1 and itself that is a factor of 279.

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5. Which number is divisible by 4?  386, 418, 568, 694

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6. Which number is divisible by 6?  496, 246, 589, 634

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7. Write twelve squared in standard form.

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8. Write eight cubed in standard form.

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9. The numbers 1, 7, 49, 343, … are each powers of 7. What is the next number in the list? 

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10. If two raised to the eleventh power is 2,048, then what is two raised to the twelfth power?

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