Composite Numbers Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

medium

How many composite numbers are there from

1

to

20

? List them and explain why each is composite.

Solution

1
Primes from $1$ to $20$ : $2, 3, 5, 7, 11, 13, 17, 19$ ( $8$ primes). The number $1$ is neither.
2
Composites: $4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20$ ( $11$ composites).
3
Each is composite because it has at least one factor other than $1$ and itself (e.g., $4 = 2^2$ , $9 = 3^2$ , $15 = 3 \times 5$ ).

Answer

There are

11

composite numbers from

1

to

20

.

From

1

to

20

:

1

number (

1

) is neither,

8

are prime, and

11

are composite. This partition of the integers into primes, composites, and

1

is fundamental — prime factorisation only works because primes are the irreducible building blocks.

About Composite Numbers

Integers greater than 1 that can be expressed as a product of two smaller positive integers; they are the opposite of primes.

Learn more about Composite Numbers →

More Composite Numbers Examples

Determine whether [formula] is prime or composite. If composite, find a factor pair.

Example 2 medium

List all composite numbers between [formula] and [formula], and for each, give one non-trivial facto

Is [formula] composite? Is [formula] composite? Is [formula] composite? Explain each briefly.

← All Composite Numbers Examples Composite Numbers Concept

Related Concepts

Prime Numbers Factors Prime Factorization Greatest Common Factor