Two marks example problems II — task. Mathematics State Board, Class 10.

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1. Can the number \(6^n\), \(n\) being a natural number, end with the digit \(5\)? Give a reason for your answer.

Answer:

\(6^n\) can end with the digit \(5\).
\(6^n\) cannot end with the digit \(5\).

Reason:

\(6^n\) has the multiples that can end with the digit \(5\).
\(6^n\) has the factor \(2\) and so it must be an even number.

2. Is \(7 \times 5 \times 3 \times 2 + 3\) a composite number. Justify your answer.

Answer:

not a composite number
composite number

Reason:

Since it has the factors one and itself.
Since it has more than two factors.

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