Weili wanted to pack $60$ apples and $75$ pears into as many bags as possible, with no remainder. She packed the same number of fruit in each bag. The number of apples in each bag was the same. How many apples were there in each bag? 
Overseas Competition->Knowledge Point->Number Theory Modules->Factors and Multiples->Common Factors and Common Multiples
Factors of $60$: $1$, $2$, $3$, $4$, $5$, $6$, $10$, $12$, $15$, $20$, $30$ and $60$,  Factors of $75$: $1$, $3$, $5$, $15$, $25$ and $75$,  Since Weili wanted to pack the apples and pears into as many bags as possible, we need to choose the largest common factor of both $60$ and $75$.  Largest common factor $\rightarrow 15$,  Hence, Weili should use $15$ bags. Number of apples in each bag$\rightarrow60\div15$  $=4$. 