The square roots of square triangular numbers, $U_n$, are split into two special coprime factors called the ‘major’ and the ‘minor’ factor, denoted by $μ_n$ and $λ_n$. These factors on their own form two distinct sequences. Explicit formulae for $μ_n$ and $λ_n$ are established, in purely algebraic form as well as in hyperbolic function form. A large number of sundry properties of $μ_n$ and $λ_n$ are established. Finally, an application of Major factors in obtaining a reduction formula for $U_n$ is demonstrated. (orig.)