can we have any n € N, where 7^n ends with the digit zero?
Answers
7¹ = 7
7² = 49
7³ = 343
7⁴ = 2401
7⁵ = 16807
Thus, the unit digits repeat themselves after 5 th power of 7. Till tjen, no zero unit digit occurs. Then for any natural number n, 7ⁿ does not end in 0.
Answer:
If 7n has to end with the digit 0 for any natural number n, then it has to be divisible by 10. ie. its prime factorisation should have the factors of both 2 and 5 [ since 10=2x5 ] But we know that 7=7x1 By the fundamental theorem of arithmetics, we also know that there exist no other factors for 7. Thus we conclude that 7n cannot end with the digit 0 for any natural number n.Read more on Sarthaks.com - https://www.sarthaks.com/2136/show-that-the-number-of-the-form-7-n-n-n-cannot-have-unit-digit-zero.
Step-by-step explanation:
Hm. let me help to know whether this is right or wrong☺