Question

why the number 4n where n is a natural number cannot end with 07​

Answer 1

Answer:

given" n" is a rational number.

Let 4^n ends with zero. then 4 is divisible by 5 but prime factors of 4 are 2 × 2.

4^n= (2×2)^n=2^2n

thus prime factorization of 4^n does not contain 5 .so the uniqueness of the fundamental theorem of arithmetic guarantees that there are no other primes in the factorization of 4^n.

hence there is no natural number"n" for which 4^n ends with the digit zero.

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