Sa sipnayan, ang sinasabing nahahati o pahati ang isang buumbilang ${\displaystyle m}$ ng ${\displaystyle n}$, kung may isa pang bilang na mapaparami sa ${\displaystyle m}$ upang maging bunga ng dalawa ang ${\displaystyle n}$. Ito ang siyang tinatawag na pagkahatiin ng mga bilang.

Sinasabing pahati ng isang bilang ${\displaystyle n}$ ang isang buumbilang ${\displaystyle m}$ kung mayroong isang buumbilang ${\displaystyle k}$ kung saan ${\displaystyle n=mk}$. Isinusulat ito bilang

${\displaystyle m\mid n}$

at kung hindi,

${\displaystyle m\not \mid n.}$.^[1][2]

Sa lahat ng buumbilang ${\displaystyle a,b,c}$:

• Kung ${\displaystyle a\mid b}$ at ${\displaystyle b\mid c,}$ sagayon ${\displaystyle a\mid c;}$ alalaong baga, palipat ang pagkahatiin.
• Kung ${\displaystyle a\mid b}$ at ${\displaystyle b\mid a,}$ sagayon ${\displaystyle a=b}$ o ${\displaystyle a=-b.}$
• Kung ${\displaystyle a\mid b}$ and ${\displaystyle a\mid c,}$ sagayon ${\displaystyle a\mid (b+c)}$ at ${\displaystyle a\mid (b-c).}$^[a] Subali’t kung ${\displaystyle a\mid b}$ at ${\displaystyle c\mid b,}$ hindi laging totoo na ${\displaystyle (a+c)\mid b}$ (halimbawa, ${\displaystyle 2\mid 6}$ at ${\displaystyle 3\mid 6}$ nguni’t di pahati ng 5 ang 6).
• ${\displaystyle a\mid b\iff ac\mid bc}$ sa di-serong ${\displaystyle c}$. Sumasakatuwid ito sa katotohanang ${\displaystyle ka=b\iff kac=bc}$.

1. ↑ ${\displaystyle a\mid b,\,a\mid c}$ ${\displaystyle \Rightarrow \exists j\colon ja=b,\,\exists k\colon ka=c}$ ${\displaystyle \Rightarrow \exists j,k\colon (j+k)a=b+c}$ ${\displaystyle \Rightarrow a\mid (b+c).}$ Gayundin, ${\displaystyle a\mid b,\,a\mid c}$ ${\displaystyle \Rightarrow \exists j\colon ja=b,\,\exists k\colon ka=c}$ ${\displaystyle \Rightarrow \exists j,k\colon (j-k)a=b-c}$ ${\displaystyle \Rightarrow a\mid (b-c).}$