Number Theory

Lesson

In the statement $3\times5=15$3×5=15 we have a product (which is the answer of $15$15), and a factor pair of $3$3 and $5$5. The numbers that multiply together to give us the product are factors, when we have 2 of them that multiply to give us a product they are a factor pair. There is another factor pair for 15. Can you find it?

Sometimes there is more than one factor pair. For example, the number 12. Could be written as

$2\times6=12$2×6=12

$3\times4=12$3×4=12

$1\times12=12$1×12=12

So $12$12 has $3$3 factor pairs. 2 and 6, 1 and 12, 3 and 4.

Every number will have at least one factor pair. Prime numbers have **only one** factor pair, of $1$1 and itself. For example $7$7. It's only factor pair is $1$1 and $7$7.

Let's find the factor pairs for the number $6$6.

$\times$× | $1$1 | $2$2 | $3$3 | $4$4 | $5$5 | $6$6 |
---|---|---|---|---|---|---|

$1$1 | $1$1 | $2$2 | $3$3 | $4$4 | $5$5 | $6$6 |

$2$2 | $2$2 | $4$4 | $6$6 | $8$8 | $10$10 | $12$12 |

$3$3 | $3$3 | $6$6 | $9$9 | $12$12 | $15$15 | $18$18 |

$4$4 | $4$4 | $8$8 | $12$12 | $16$16 | $20$20 | $24$24 |

$5$5 | $5$5 | $10$10 | $15$15 | $20$20 | $25$25 | $30$30 |

$6$6 | $6$6 | $12$12 | $18$18 | $24$24 | $30$30 | $36$36 |

Using the table we can find all the numbers that multiply to give $6$6. We will only count factor pairs once, so, $1\times6$1×6is the same as $6\times1$6×1. So $1$1 and $6$6 are one set of factors for the number $6$6.

Using the table, what are the other factor pairs of $6$6?

Using the table we can look for all the numbers that multiply together to give $6$6.

The factor pairs of 6 are:

- 1 and 6, &
- 2 and 3.

$59$59 is a *prime* number.

Which of the following options is a factor pair of $59$59?

$56$56 and $3$3

A$1$1 and $59$59

B$56$56 and $3$3

A$1$1 and $59$59

B

If we multiply $4$4 by $14$14, we get $56$56, so $4$4 and $14$14 make a factor pair of $56$56.

Which of the following options is also a factor pair of $56$56?

$14$14 and $2$2

A$4$4 and $7$7

B$8$8 and $7$7

C$2$2 and $2$2

D$14$14 and $2$2

A$4$4 and $7$7

B$8$8 and $7$7

C$2$2 and $2$2

D

Complete the table below, listing all factor pairs of the number $15$15.

Factor pairs of $15$15 $\left(1,\editable{}\right)$(1,) $\left(\editable{},5\right)$(,5) Is $15$15 prime or composite?

$15$15 is a composite number.

A$15$15 is a prime number.

B$15$15 is a composite number.

A$15$15 is a prime number.

B

Use a range of multiplicative strategies when operating on whole numbers