Mathematics
Check whether 6n can end with the digit 0 for any natural number n.
Real Numbers
7 Likes
Answer
If the number 6n, for any natural number n, ends with digit 0, then it would be divisible by 5. That is, the prime factorization of 6n would contain the prime number 5. This is not possible because 6n = (2 x 3)n; so the only primes in the factorization of 6n are 2 and 3 and the uniqueness of the Fundamental Theorem of Arithmetic guarantees that there are no other primes in the factorization of 6n. So, there is no natural number n for which 6n ends with the digit zero.
Answered By
5 Likes
Related Questions
Find the L.C.M. and H.C.F. of the following integers by applying the prime factorisation method.
(i) 12, 15 and 21
(ii) 17, 23 and 29
(iii) 8, 9 and 25
Given that HCF (306, 657) = 9, find LCM (306, 657).
Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.
There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?