first try. passed all except 999999937(TLE)

ProductOfDigits.cpp

class ProductOfDigits {
    public:
    int smallestNumber(int N) {
        vector<int> factors;
        int n = N;
        for(int i=2;i<=N;++i){
            while(n%i==0){
                factors.push_back(i);
                n/=i;
            }
            if(n==1) break;
        }

        if(factors.size()==0) return 1; // 1

        int ret=0, c=1;
        for(auto f : factors){
            if(f>9) return -1; //2 digits factor
            c *= f;
            if(c>9){
                c=f;
                ret++;
            }
        }
        if(c>1) ret++; //last one
        return ret;
    }
};