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If $a$ and $b$ are positive integers with $a\le b$ and $a^2\equiv a\mathrm{mod}b$, then the set $$M_{a,b}=\{x\in \mathbb{N}:x\equiv a\mathrm{mod}b\text{or}x=1\}$$ is a multiplicative monoid known as an arithmetical congruence monoid (or ACM). For any monoid $M$ with units $M^{\times }$ and any $x\in M\setminus M^{\times }$ we say that $t\in \mathbb{N}$ is a factorization length of $x$ if and only if there exist irreducible elements $y_1,...,y_t$ of $M$ and $x=y_1\cdots y_t$. Let $ℒ\left(x\right)=\{t_1,...,t_j\}$ be the set of all such lengths (where $t_i\<t_{i+1}$ whenever $i\<j$). The Delta-set of the element $x$ is defined as the set of gaps in $ℒ\left(x\right)$: $\Delta \left(x\right)=\{t_{i+1}-t_i:1\le i\<k\}$ and the Delta-set of the monoid $M$...