Looking for a Unsorted Math Worksheet Templates? Download it for free!

Number Theory I Junior Math Circles - University Of Waterloo Faculty Of Mathematics Worksheet With Answers Page 6

Problem Set

1. Ms. Timson wants to split her Grade 9 math class of 36 students into groups

for an upcoming assignment. List all the possibilities of groups, each with the

same number of students, that Ms. Timson can divide her class into so that no

students are left without a group.

2. What is the ﬁrst prime number greater than 200?

3. Draw two diﬀerent factor trees for the number 100. (Start with two diﬀerent

pairs of factors.)

4. The volume of a cereal box is 1925 cm . What are the diﬀerent possible dimen-

sions of the cereal box?

(Note: The volume of a rectangular box is length

width

height.)

5. The eight digit number 1234 678 is divisible by 11. What is the digit

6. The four digit number 43

is divisible by 3, 4 and 5. What are the last two

digits?

7. (a) If a number is divisible by 2 and 3, is it always divisible by 6?

(b) If a number is divisible by 2 and 4, is it always divisible by 8?

8. What is the smallest number that you must multiply 48 by so that the product

is divisible by 45?

9. The product of three diﬀerent positive integers is 144. What is the maximum

possible sum of these three integers?

10. The digits 1, 2, 3, 4, 5 and 6 are each used once to compose a six digit number

abcdef , such that the three digit number abc is divisible by 4, bcd is divisible

by 5, cde is divisible by 3 and def is divisible by 11. Determine all possible

assignments of the digits to the letters.

11. What is the smallest number that you must multiply 1512 by in order to get a

perfect square.

A perfect square is a number that is equal to another number multiplied by

itself. For example 6

6 = 36 is a perfect square.

12. If x and y are two-digit positive integers with xy = 555, what is x + y?

Number Theory I Junior Math Circles - University Of Waterloo Faculty Of Mathematics Worksheet With Answers Page 6