120's remainder

Number Theory Level 3

The remainder when 120 is divided by single-digit integer $\color{#20A900}m$ is positive, as is the remainder when 120 is divided by single-digit integer $\color{#EC7300}n$ .

If $\color{#D61F06}m > n$ , what is the remainder when 120 is divided by $\color{#D61F06}m - n =?$

The answer is 0.

1 solution

Hana Wehbi
Jul 14, 2017

Recall the single digit integers $1,2,3,4,5,6,7,8,9$ .

Notice that $120$ is divisible by most of them except for $9$ and $7$ .

Thus, let $m=9$ and $n=7\implies m-n=2\implies 2 | 120 \implies R=0$ . Where $R$ is the reminder.

120's remainder

The answer is 0.

1 solution

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