Question

What are the prime numbers between 20-30?

Answer 1

Hint: To find the prime numbers between 20-30, we must know that prime numbers are the positive integers having only two factors, 1 and the integer itself. We will have to list the numbers between 20 and 30 along with their factors. Then, we have to select the prime numbers out of it.

Complete step by step solution:
We have to find the prime numbers between 20-30. Let us first recall what prime numbers are. Prime numbers are the positive integers having only two factors, 1 and the integer itself. Let us list the factors of each number.
Factors of 20: 1, 2, 4, 5, 10, 20
Factors of 21: 1, 3, 7, 21
Factors of 22: 1, 2, 11, 22.
Factors of 23: 1, 23.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 25: 1, 5, 25
Factors of 26: 1, 2, 13, 26
Factors of 27: 1, 3, 9, 27
Factors of 28: 1, 2, 4, 7, 14, 28
Factors of 29: 1, 29
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30
We can see that 23 and 29 have only 2 factors, that are, 1 and the number itself. Hence, they are the prime numbers.

Therefore, the prime numbers between 20-30 are 23 and 29.

Note: Students should never be confused with prime numbers and composite numbers. We have seen what prime numbers are. A number that is divisible by a number other than 1 and the number itself, is called a composite number. For example, from the factors listed in the solution, we can see that all the numbers except 23 and 29 are composite numbers. Students must note that 1 is neither prime nor composite.