Can the number 6 to the power n, n is a natural number, end with digit 5? Give reasons.
Answers
6ⁿ can not end with digit 5 where n is a natural number
Step-by-step explanation:
5 is a prime number
hence number to end with 5 must have a factor of 5
now lets check 6ⁿ
6 = 2 * 3
=> 6ⁿ = ( 2 * 3) ⁿ
Hence 6ⁿ has only factors of 2 & 3 ( n times)
no factor of 5 is there
Hence 6ⁿ can not end with 5
also 6 raised to power any natural number ≥ 1
end with 6 only
Hence 6ⁿ can not end with digit 5 where n is a natural number
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6ⁿ will not end with digit 5.
Step-by-step explanation:
Any number ending with 5 will be a multiple of 5.
Let's check the factors of 6.
6 = 2 * 3.
5 is not a factor of 6. So the multiples of 6 will never end with 5.
6ⁿ will never have 5 in its ones place. It will always end with 6.
For example:
6^2 = 6 * 6 = 36
6^3 = 6 * 6 * 6 = 216
6^4 = 6 * 6 * 6 * 6 = 1296
6^5 = 6 * 6 * 6 * 6 * 6 = 7776
Hence 6 to the power n, where n is a natural number, will not end with digit 5.