Question

Two positive integers ${}^{\prime }{m}^{\prime }$ and ${}^{\prime }{n}^{\prime }$ follow the conditions:

(i) $m<n$

(ii) They are not relatively prime

(iii) Their product is $13013$
Find their gcd and hence determine all such ordered pairs $(m,n).$

Answer 1

Two numbers are "relatively prime" when they have no common factors other than $1$

In other words you cannot evenly divide both by some common value.
$13013=7\times 11\times 13\times 13$
$(m,n)$ are not relatively prime. Thus, $(m,n)$ can be $(91,143)$ or $(13,1001)$
GCD of $(91,143)$ is $13$
GCD of $(13,1001)$ is $13$