If a number is divided by $45$, then the remainder is $32$. If the same number is divided by $15$, then the remainder is

Apply the congruence modulo property that if a number leaves a remainder of 32 when divided by 45, it can be expressed as 45k plus 32. Because 15 is a factor of 45, the term 45k is perfectly divisible by 15. Divide the remaining remainder 32 by 15, which gives a new quotient of 2 and a leftover remainder of 2. The final remainder is 2.

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