# 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? ANSWER BOX:  yds  RESULTS BOX:
 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? ANSWER BOX:   RESULTS BOX:
 3 Name one prime number from 70 and 79. ANSWER BOX:   RESULTS BOX:
 4 The number 279 is composite. Name a number other than 1 and itself that is a factor of 279. ANSWER BOX:   RESULTS BOX:
 5 Which number is divisible by 4?  386, 418, 568, 694 ANSWER BOX:   RESULTS BOX:
 6 Which number is divisible by 6?  496, 246, 589, 634 ANSWER BOX:   RESULTS BOX:
 7 Write twelve squared in standard form. ANSWER BOX:   RESULTS BOX:
 8 Write eight cubed in standard form. ANSWER BOX:   RESULTS BOX:
 9 The numbers 1, 7, 49, 343, ... are each powers of 7. What is the next number in the list?  ANSWER BOX:   RESULTS BOX:
 10 If two raised to the eleventh power is 2,048, then what is two raised to the twelfth power? ANSWER BOX:   RESULTS BOX: