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Show that numbers 8n can never end with digit 0 for any natural number n.

Posted by Sonal Gaur 6 years ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years ago

If any numbr ends with 0, then it must be divisible by 10 .Hence it should have 5 and 2 as a factors. Now the factorization of 8ⁿare:
$\therefore 8 ^ { n } = ( 2 \times 2 \times 2 ) ^ { n } = 2 ^ { n } \times 2 ^ { n } \times 2 ^ { n }$
Hence 5 is not in the factors of 8^n.
From the fundamental theorem of arithmetic, we know that the prime factorization of every composite number is unique.
So it is clear that 8ⁿ is not divisible by 10.
$\therefore$ 8ⁿ can never end with 0.

0Thank You

ANSWER

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