Show that 12" cannot end with the digit 0 or 5 for any natural number

1.	Show that 12" cannot end with the digit 0 or 5 for any natural number n.2
Answer» If 12n ends with 0 then it must have 5 as a factor. But, 12n=(2×2×3)n which shows that only 2 and 3 are the prime factors of 12n. Also, we know from the fundamental theory of arithmetic that the prime factorization of each number is unique. So, 5 is not a factor of 12n. Hence, 12n can never end with the digit 0. Hit like if you find it useful!

Show that 12" cannot end with the digit 0 or 5 for any natural number n.2

Answer»

If 12n ends with 0 then it must have 5 as a factor.

But, 12n=(2×2×3)n which shows that only 2 and 3 are the prime factors of 12n.

Also, we know from the fundamental theory of arithmetic that the prime factorization of each number is unique.

So, 5 is not a factor of 12n.

Hence, 12n can never end with the digit 0.

Hit like if you find it useful!