Every whole number is a multiple of its factors.

To demonstrate, let's write down the factor pairs of {\color{blue}{10}}\mathbin{:}

\qquad 1\times 10 = {\color{blue}{10}}

\qquad 2\times 5 = {\color{blue}{10}}

Therefore, the factors of {\color{blue}{10}} are as follows:

1,\quad 2,\quad 5, \quad 10

Each of these factors has 10 as a multiple:

  • The multiples of 1 are 1, \quad 2, \quad 3, \quad 4, \quad 5, \quad 6, \quad 7, \quad 8, \quad 9, \quad {\color{blue}{10}}, \quad 11,\quad \ldots \,.

  • The multiples of 2 are 2, \quad 4, \quad 6, \quad 8, \quad {\color{blue}{10}}, \quad 12,\quad \ldots \,.

  • The multiples of 5 are 5, \quad {\color{blue}{10}}, \quad 15,\quad \ldots \,.

  • The multiples of 10 are {\color{blue}{10}}, \quad 20,\quad \ldots \,.

Whenever we write down a statement regarding factors, we can always write down a related statement about multiples.

For example, the following two statements are equivalent (mean the same thing):

  • {\color{blue}{10}} is a multiple of {\color{red}{2}}

  • {\color{red}{2}} is a factor of {\color{blue}{10}}

FLAG

Which of the following numbers has 11 as a multiple?

  1. 8
  2. 11
  3. 22
EXPLANATION

Every whole number is a multiple of its factors. For example, the following two statements are equivalent (mean the same thing):

  • {\color{blue}{18}} is a multiple of {\color{red}{3}}

  • {\color{red}{3}} is a factor of {\color{blue}{18}}

Notice that 11 is prime. Therefore, it has only two factors, namely 1 and itself: 1,\quad 11

From the given options, the only number that is in our list above is 11.

FLAG

Which of the following numbers does not have $10$ as a multiple?

a
$1$
b
$2$
c
$4$
d
$5$
e
$10$

Which of the following numbers has $17$ as a multiple?

a
$34$
b
$7$
c
$9$
d
$3$
e
$17$

Which of the following numbers does not have 12 as a multiple?

  1. 6
  2. 4
  3. 10
EXPLANATION

Every whole number is a multiple of its factors. For example, the following two statements are equivalent (mean the same thing):

  • {\color{blue}{18}} is a multiple of {\color{red}{3}}

  • {\color{red}{3}} is a factor of {\color{blue}{18}}

First, we write down the factor pairs of 12\mathbin{:}

\qquad 12 = 1 \times 12

\qquad 12 = 2 \times 6

\qquad 12 = 3 \times 4

Therefore, the factors of 12 are as follows: 1, \quad 2, \quad 3, \quad 4, \quad 6, \quad 12

Each of these numbers has 12 as a multiple.

From the given options, the only number that is not on our list above is 10.

FLAG

Which of the following numbers does not have $24$ as a multiple?

a
$9$
b
$24$
c
$3$
d
$8$
e
$6$

Which of the following numbers does not have $36$ as a multiple?

a
$12$
b
$3$
c
$7$
d
$9$
e
$6$
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