利用分解因式说明：(25^7)-(5^12)能被600整除.

(25^7)-(5^12)
=(5^2)^7-5^12
=5^14-5^12
=5^12(5^2-1)
=24*5^12
=12*5^2*5^10*2
=(12*5^2*2)*2^10
=600*2^10
所以(25^7)-(5^12)能被600整除

25^7-5^12
=25^7-5^(2*6)
=25^7-25^6
=25^5*(25^2-25)
=25^5*(625-25)
=600*25^5
所以25^7-5^12能被600整除.

5^12=25^6
(25^7)-(25^6)=(25^6)(25-1)
=(25^6)*24=(25^5)*25*4*6=25^54*600

=5^14-5^12
=(5^7-5^6)(5^7+5^6)
=5^12*(5-1)(5+1)
=4*6*5*5*5^10
=600*5^10

25^7-5^12
=(5^2)^7-5^12
=5^14-5^12
=5^12(5^2-1)
=5^12*24
=5^10*600
这个数肯定是600的倍数了
所以能被600整除，且商就是5^10

(25^7)-(5^12)
=5^14-5^12
=5^12(5^2-1)
=5^12(25-1)
=(5^12)*24
=24*(5^2)*(5^12)
=600(5^12)