Check whether 15*n can end with digit zero for any natural number
shaurychdback:
there is no number
Answers
Answered by
1043
If 15ⁿ end with digit zero,then the number should be divisible by 2 and 5.
As 2×5=10
→This means the prime factorization of 15ⁿ should contain prime factors 2 and 5.
→15ⁿ = (3×5)ⁿ
It does not have the prime factor 2 but have 3 and 5,
Since 2 is not present in the prime factorization, there is no natural number nor which 15ⁿ ends with digit zero.
So,15ⁿ can not end with digit zero.
Hope it helps
As 2×5=10
→This means the prime factorization of 15ⁿ should contain prime factors 2 and 5.
→15ⁿ = (3×5)ⁿ
It does not have the prime factor 2 but have 3 and 5,
Since 2 is not present in the prime factorization, there is no natural number nor which 15ⁿ ends with digit zero.
So,15ⁿ can not end with digit zero.
Hope it helps
Answered by
303
As we know that
15n = (3 x 5)n
= 3n x 5n
The prime factorization of 15 doesn't have a 2 and 5 as its factor. So, its factorization will never end in 10 as a number ending in 10 must have a factors as 5 and 2. So, 15n will never end in zero as 15 doesn't has 2 as a factor.
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