Question

SHOW THAT 12n CANNOT END WITH 0 OR 5 FOR ANY NATURAL NUMBER n

Answer 1

Answer:

Step-by-step explanation:

12n can only end with digits 0 or 5 when it base prime factors include 2 or 5 as its factors.

But 12 has not 2 and 5 as its prime factors. So it is impossible for 12n to end with the digit 0 or 5.

Answer 2

Answer:

Step-by-step explanation:

12 to the power of n cannot end with 0 or 5 for any value of n since the prime factorisation of 12 can be expressed as 2^2 x 3.For any number to the power of n to can end with zero only if contain both 2 and 5 as factors.

However the uniqueness of fundamental theorem of arithmetic guarantees than there is no prime factor of 12 other than 2 or 3.

Hence 12 to the power of n cannot end with 0 for any value of n