Question

show that 5 raise to N cannot end with the digit 2 for any natural number N

Answer 1

if 5 n were to end with digit 2 , then it would be divisible by digit 2 , or it would have 2 in it's prime factorisation . but the prime factorisation of 5 is 1×5 , and this factorisation is guaranteed by fundamental theorem of arithmetic ; therefore there is no natural number for n so that 5 n can end with digit 2