Multiples and factors

Advanced Math 4 · Unit 3 · factors-multiples-intro · Teacher edition

factors-multiples-intro

Name ______________________________Date ______________

1.
How many factors does $24$ have? Count $1$ and $24$ themselves.
Answer: ______________
2.
List all the factors of $36$ in pairs. What is the sum of all the factors of $36$ ?
Answer: ______________
3.
Which of these numbers is prime?
1. (A)
  $1$
2. (B)
  $51$
3. (C)
  $53$
4. (D)
  $91$

Answer key — Multiples and factors

1.
8factors-multiples-intro-01
Factor pairs of $24$ : $1 \times 24$ , $2 \times 12$ , $3 \times 8$ , $4 \times 6$ . That is $1, 2, 3, 4, 6, 8, 12, 24$ — $\mathbf{8}$ factors.
2.
91factors-multiples-intro-02
Pairs: $1 \times 36$ , $2 \times 18$ , $3 \times 12$ , $4 \times 9$ , $6 \times 6$ . Factors: $1, 2, 3, 4, 6, 9, 12, 18, 36$ . Sum: $1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 + 36 = \mathbf{91}$ .
3.
(C)
$53$
factors-multiples-intro-03
$53$ has no factor among $2, 3, 5, 7$ , so it is prime: $\mathbf{53}$ . ( $1$ has only one factor, so it is not prime; $51 = 3 \times 17$ and $91 = 7 \times 13$ are odd but composite.)