Is 63 prime or composite?

Understand the Problem

The question is asking whether the number 63 is a prime or composite number. A prime number is one that has exactly two distinct positive divisors (1 and itself), while a composite number has more than two positive divisors. To solve this, we will check the factors of 63.

Answer

63 is a composite number.

Steps to Solve

Identify the factors of 63

To determine whether 63 is prime or composite, we need to identify its factors. A factor is a number that divides another number without leaving a remainder.

List potential factors

We should consider all numbers from 1 up to the square root of 63. The square root of 63 is approximately 7.94, so we will check the integers from 1 to 7.

Check divisibility of each number

We will check which numbers between 1 and 7 divide 63 evenly:

$63 \div 1 = 63$ (1 is a factor)
$63 \div 2 = 31.5$ (not a factor)
$63 \div 3 = 21$ (3 is a factor)
$63 \div 4 = 15.75$ (not a factor)
$63 \div 5 = 12.6$ (not a factor)
$63 \div 6 = 10.5$ (not a factor)
$63 \div 7 = 9$ (7 is a factor)

The factors of 63 found are: 1, 3, 7, 9, 21, and 63.

Count the number of distinct factors

Now we count the total number of distinct factors: 1, 3, 7, 9, 21, 63 are six factors. Since 63 has more than two distinct factors, we conclude that it is a composite number.

63 is a composite number.

More Information

Since 63 has multiple factors, such as 3 and 7 (both of which multiply to give back 63), it is classified as a composite number. The sum of the factors (1 + 3 + 7 + 9 + 21 + 63) equals 104, which is an interesting piece of information about its nature.

Tips

A common mistake is to overlook the factors that are not immediately obvious. It's important to consider all integers up to the square root of the number when determining factors.
Another mistake is to assume that the number is prime just because it is odd; odd numbers can also be composite.

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