Determine gcd (65, 1001). Hence write the ratio 65 ∶ 1001 in its simplest form.
The factors of 65 are $\{1, 5, 13, 65\}$. The factors of 1001 are $\{1, 7, 11, 13, 77, 91, 143, 1001\}$. Therefore the gcd is 13. The ratio is simply a factor and simplified as follows:
$$65:1001 \quad = \quad \frac{65}{13}:\frac{1001}{13} \quad = \quad 5:77$$