How many prime numbers are there from 21 to 30? How many composite numbers are there from 21 to 30?

Question

Homi · Accepted Answer

Let us find all the prime and composite numbers between 21 and 30.

Step 1 — List all numbers

First, we list all the numbers from 21 to 30.

$21, 22, 23, 24, 25, 26, 27, 28, 29, 30$

Diagram 1

Step 2 — Understand prime and composite numbers

A prime number can only be divided exactly by 1 and itself. It has only two factors. A composite number can be divided exactly by more than 1 and itself. It has more than two factors. Let us check each number one by one.

Step 3 — Check each number from 21 to 30

Let us check 21. We can divide 21 by 1, 3, 7, and 21. It has more than two factors. So, 21 is a composite number.

Let us check 22. We can divide 22 by 1, 2, 11, and 22. It has more than two factors. So, 22 is a composite number.

Let us check 23. We can only divide 23 by 1 and 23. It has only two factors. So, 23 is a prime number.

Let us check 24. We can divide 24 by 1, 2, 3, 4, 6, 8, 12, and 24. It has more than two factors. So, 24 is a composite number.

Let us check 25. We can divide 25 by 1, 5, and 25. It has more than two factors. So, 25 is a composite number.

Let us check 26. We can divide 26 by 1, 2, 13, and 26. It has more than two factors. So, 26 is a composite number.

Let us check 27. We can divide 27 by 1, 3, 9, and 27. It has more than two factors. So, 27 is a composite number.

Let us check 28. We can divide 28 by 1, 2, 4, 7, 14, and 28. It has more than two factors. So, 28 is a composite number.

Let us check 29. We can only divide 29 by 1 and 29. It has only two factors. So, 29 is a prime number.

Let us check 30. We can divide 30 by 1, 2, 3, 5, 6, 10, 15, and 30. It has more than two factors. So, 30 is a composite number.

Step 4 — Count the prime numbers

The prime numbers we found are 23 and 29. Let us count them.

$\text{Number of prime numbers} = 2$

$\boxed{2 \text{ prime numbers}}$

Step 5 — Count the composite numbers

The composite numbers we found are 21, 22, 24, 25, 26, 27, 28, and 30. Let us count them.

$\text{Number of composite numbers} = 8$

$\boxed{8 \text{ composite numbers}}$

Answer

(i) There are 2 prime numbers (23, 29) from 21 to 30. (ii) There are 8 composite numbers (21, 22, 24, 25, 26, 27, 28, 30) from 21 to 30.

Question 8

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