Composite Numbers, Prime Numbers, And 1 Worksheet (Page 2 of 3) in pdf

Composite Numbers, Prime Numbers, And 1 Worksheet Page 2

Some Divisibility Problems

If a and b are positive integers, then we say that b divides a and also that a is divisible by b if

there is a number q such that a = qb. The number q is the quotient of a by b. To write “b divides

a” with symbols, we write b a. When b does not divide a, we write b a.

Examples. 4 12, and 13 91, but 12 25.

1. Which of the following numbers divides 2

(a) 2

(b) 5

(d) 9

Why? (Or why not?)

2. Which of the following is true (and why!):

(a) If a number is divisible by both 3 and 4, then it must be divisible by 3 4 = 12.

(b) If a number is divisible by 4 and 6, then it must be divisible by 4 6 = 24.

3. (a) If a number N is not divisible by 3, is it possible that 2N is divisible by 3?

(b) The number 15N is divisible by 6. Does N have to be divisible by 6?

4. Prove that the product of ﬁve consecutive natural numbers is:

... divisible by 30.

i. ii. ... divisible by 120.

5. Check whether the number 24681357975318642 is divisible by:

(a) 2

(b) 4

(d) 10

(e) 3

(f) 9

(g) 11

(h) 7

6. An agent at an incompetent intelligence agency was using a code where each number is

assigned a distinct letter of the alphabet. The agent writes AB

CD = EEF F . Prove that

the agent is wrong.

Composite Numbers, Prime Numbers, And 1 Worksheet Page 2