Question

Q13. Show that 7" can not end with the digit zero. for any natural number n.​

Answer 1

Answer:

Let us assume that 7ⁿ ends with the digit zero.

If a number has to end with zero, it is important that it is divisible by both 5 and 2.

But 6 is not divisible by both 5 and 2.

Hence, as 5 and 2 aren't present in the prime factorisation of 7, then 7ⁿ doesn't end with zero.

More to know :

• Euclid's Division Lemma :

Let two positive integers a and b, there exist two integers q and r, satisfying a = bq + r, 0 ≤ r ≤ b.

• Numbers divisible by itself and 1 is called prime numbers.

• Numbers that are divisible by itself, 1 and any other number is called composite numbers.