What can 13 be divided by?

Understand the Problem

The question is asking for the divisors of the number 13, which means we need to identify all the whole numbers that can divide 13 without leaving a remainder.

Answer

The divisors of 13 are $1$ and $13$.

Steps to Solve

Identify the definition of divisors

Divisors are whole numbers that can divide another number without leaving a remainder.

List potential divisors

For the number 13, we need to check for whole numbers from 1 up to 13 to see which can divide 13 evenly.

Test each number

We will test each number from 1 to 13:

For $1$: $13 \div 1 = 13$ - remainder is $0$
For $2$: $13 \div 2 = 6.5$ - remainder is not $0$
For $3$: $13 \div 3 \approx 4.33$ - remainder is not $0$
For $4$: $13 \div 4 = 3.25$ - remainder is not $0$
For $5$: $13 \div 5 = 2.6$ - remainder is not $0$
For $6$: $13 \div 6 \approx 2.17$ - remainder is not $0$
For $7$: $13 \div 7 \approx 1.857$ - remainder is not $0$
For $8$: $13 \div 8 = 1.625$ - remainder is not $0$
For $9$: $13 \div 9 \approx 1.444$ - remainder is not $0$
For $10$: $13 \div 10 = 1.3$ - remainder is not $0$
For $11$: $13 \div 11 \approx 1.182$ - remainder is not $0$
For $12$: $13 \div 12 \approx 1.083$ - remainder is not $0$
For $13$: $13 \div 13 = 1$ - remainder is $0$

Summarize divisors

From our tests, the numbers that divide 13 evenly are $1$ and $13$.

The divisors of 13 are $1$ and $13$.

More Information

Since 13 is a prime number, it has exactly two divisors: $1$ and itself. This is a defining property of prime numbers.

Tips

A common mistake is to include $0$ as a divisor, but division by zero is undefined.
Another mistake is misunderstanding the definition of even and odd divisions, which can lead to incorrect conclusions.

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