Understanding What Makes the Number 75 a Composite Number
A composite number is defined as a positive integer that has at least one positive divisor other than one and itself. Unlike prime numbers, composite numbers can be divided evenly by numbers other than 1 and the number itself. Let's delve into why 75 is classified as a composite number.
The Definition of Composite Numbers
A composite number is a natural number that can be expressed as a product of two smaller natural numbers other than 1 and itself. This means that it has more than two distinct factors. The opposite of a composite number is a prime number, which has exactly two distinct positive divisors: 1 and the number itself.
Divisors and Factors of 75
For the number 75, we can identify its divisors and factors to determine if it meets the criteria to be classified as a composite number. The divisors of 75 are 1, 3, 5, 15, 25, and 75. The factors of 75 can be factored into prime numbers as follows:
75 3 × 52
Since 75 has divisors other than 1 and itself, such as 3, 5, 15, and 25, it meets the criteria for being a composite number. Therefore, 75 is classified as a composite number because it has multiple factors beyond 1 and 75.
Dividing 75
To further illustrate why 75 is a composite number, consider the following:
75 can be divided by 3, 5, 15, 25, and 75 itself. Specifically, if we divide 75 by 3, we get:
75 ÷ 3 25
If we divide 75 by 5, we get:
75 ÷ 5 15
These divisions show that 75 has multiple divisors other than 1 and itself, confirming that it is a composite number.
Definition and Classification of Natural Numbers
Natural numbers can be classified into three subsets:
Composite numbers Prime numbers 1, which is neither prime nor compositeA number is considered composite if it can be expressed as a multiplication of prime numbers. Conversely, a number is prime if its only divisors are 1 and the number itself. Based on this definition, 75 is a composite number because it can be expressed as:
75 3 × 5 × 5
Furthermore, the factors of 75 are 1, 3, 5, 15, 25, and 75, which confirms that 75 is indeed a composite number with more than two distinct factors.