2.4 Find multiples and factors  (Page 2/9)

[link] highlights the multiples of $10$ between $1$ and $50.$ All multiples of $10$ all end with a zero.

[link] highlights multiples of $3.$ The pattern for multiples of $3$ is not as obvious as the patterns for multiples of $2,5,\text{and}10.$

Unlike the other patterns we’ve examined so far, this pattern does not involve the last digit. The pattern for multiples of $3$ is based on the sum of the digits. If the sum of the digits of a number is a multiple of $3,$ then the number itself is a multiple of $3.$ See [link] .

Consider the number $42.$ The digits are $4$ and $2,$ and their sum is $4+2=6.$ Since $6$ is a multiple of $3,$ we know that $42$ is also a multiple of $3.$

Look back at the charts where you highlighted the multiples of $2,$ of $5,$ and of $10.$ Notice that the multiples of $10$ are the numbers that are multiples of both $2$ and $5.$ That is because $10=2\cdot 5.$ Likewise, since $6=2\cdot 3,$ the multiples of $6$ are the numbers that are multiples of both $2$ and $3.$

Use common divisibility tests

Another way to say that $375$ is a multiple of $5$ is to say that $375$ is divisible by $5.$ In fact, $375÷5$ is $75,$ so $375$ is $5\cdot 75.$ Notice in [link] that $\mathrm{10,519}$ is not a multiple $3.$ When we divided $\mathrm{10,519}$ by $3$ we did not get a counting number, so $\mathrm{10,519}$ is not divisible by $3.$

Since multiplication and division are inverse operations, the patterns of multiples that we found can be used as divisibility tests. [link] summarizes divisibility tests for some of the counting numbers between one and ten.