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.

63 is a composite number.

63 is a composite number.

Steps to Solve

1. 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.

1. 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.

1. 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.

1. 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.