# I am thinking of a number. If I divide the number by 6, I have a remainder of 4. If I divide the number by 8, I have a remainder of 6. What is the smallest possible number?

Jan 28, 2017

22

#### Explanation:

the number $\div 6 \to$ remainder of 4

So: $\text{something "xx6+"remainder of 4 = the number}$

$2 \times 6 = 12 \text{ } + 4 = 16$
$\textcolor{red}{3 \times 6 = 18 \text{ } + 4 = 22}$
$4 \times 6 = 24 \text{ } + 4 = 28$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
the number $\div 8 \to$ remainder of 6

So: $\text{something "xx8+"remainder of 6 = the number}$

$\textcolor{red}{2 \times 8 \text{ } + 6 = 22}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The least number is 22

The use of the word 'smallest' produces problems mathematically. It is not good practice to use 'smallest'.