# Without Actual Division Show that Each of the Following Rational Numbers is a Non-terminating Repeating Decimal (I) 73/(2^3× 3^3 × 5) - Mathematics

Without actual division show that each of the following rational numbers is a non-terminating repeating decimal

(i) 73/(2^3× 3^3 × 5)

#### Solution

73/(2^3× 3^3 × 5)

We know 2, 3 or 5 is not a factor of 73, so it is in its simplest form.
Moreover, (22× 33 ×5) ≠ (2m × 5n
Hence, the given rational is non-terminating repeating decimal.

Concept: Euclid’s Division Lemma
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