Composite Numbers Math Example 2

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

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List all composite numbers between

20

and

35

, and for each, give one non-trivial factor pair.

1
List all integers $21$ – $34$ and identify composites (primes in this range: $23, 29, 31$ ).
2
$21 = 3 \times 7$ , $22 = 2 \times 11$ , $24 = 4 \times 6$ , $25 = 5 \times 5$ , $26 = 2 \times 13$ , $27 = 3 \times 9$ , $28 = 4 \times 7$ , $30 = 5 \times 6$ , $32 = 4 \times 8$ , $33 = 3 \times 11$ , $34 = 2 \times 17$ .
3
Primes $23, 29, 31$ are excluded from the composite list.

Answer

Composites in

(20, 35)

21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34

with factor pairs as listed.

A composite number has at least one factor besides

1

and itself. Systematically checking each number and excluding primes reveals the composites. Between

20

and

35

, three primes (

23, 29, 31

) are interspersed among the composites.

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.

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

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

How many composite numbers are there from [formula] to [formula]? List them and explain why each is