13. (9 points) The number of simplest fractions less than 8 with a denominator of 24 is $\qquad$; the sum of these simplest fractions is $\qquad$
【Solution】Solution: $24=2^{3} \times 3$
$8 \times 24=192$ All numbers less than 192 and not divisible by $2, 3$ are the numerators that satisfy the condition, which means the total number of $N$ for $6 \mathbf{N}+1<192$ and $6 \mathbf{N}+5<192$ (where $N$ is a natural number). $6 \mathbf{N}+1<192$ solves to $N<32$, meaning all natural numbers less than 32 are valid, i.e., 32. Similarly, $6 \mathbf{N}+5<192$ solves to $N<32$, and the number of $N$ is also 32. Therefore: $32+32=64$ (numbers)

From the two inequalities above, we know that the numerators of the simplest fractions with a denominator of 24 and less than 8 are composed of two arithmetic sequences, one being $1,7,13 \cdots$, and the other being $5,11,17 \cdots$, both with a common difference of 6, and each having 32 terms. Using the sum formula for an arithmetic sequence, we get: $32 \times 1+[32 \times(32-1) \times 6] \div 2=3008$ $32 \times 5+[32 \times(32-1) \times 6] \div 2=3136$

The sum of the numerators is: $3008+3136=6144$
The sum of these simplest fractions is: $6144 \div 24=256$
Therefore, the answers are: 64,256.