Are the following number prime or composite. show by finding the factor (a ) 48
The Correct Answer and Explanation is:
Answer:
The number 48 is composite.
Explanation:
To determine whether a number is prime or composite, we must examine how many positive factors it has. A prime number has exactly two distinct positive factors: 1 and itself. A composite number has more than two positive factors.
Let’s examine the number 48.
Start by finding its factors. A factor is a number that divides evenly into another number. We look for all whole numbers that divide 48 without leaving a remainder:
- 1 × 48 = 48
- 2 × 24 = 48
- 3 × 16 = 48
- 4 × 12 = 48
- 6 × 8 = 48
So the positive factors of 48 are:
1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Clearly, 48 has more than two factors. That means it is not a prime number. Therefore, 48 is a composite number.
Another way to show this is by breaking 48 into its prime factorization. This involves writing it as a product of only prime numbers:
48 ÷ 2 = 24
24 ÷ 2 = 12
12 ÷ 2 = 6
6 ÷ 2 = 3
3 ÷ 3 = 1
So, the prime factorization of 48 is:
2 × 2 × 2 × 2 × 3 or 2⁴ × 3
Again, since 48 is divisible by 2 and 3 (both smaller prime numbers), that confirms it is not a prime number.
In summary, a prime number has only two factors. Since 48 has many factors and can be divided evenly by numbers other than 1 and 48, it is a composite number.
