Understanding Prime Numbers

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Understanding Prime Numbers

Introduction

A Prime Number is a number that cannot be evenly divided by any other whole number other than 1 and itself. So 1, 2, 3 and 5 are all prime numbers, but 4 is not, since 4 can not only be divided by 1 and 4, but 2 as well.

Terms

Prime Number - A prime number is a number that cannot be evenly divided by any number other than 1 and itself.

Lesson

A prime number is a number that is not evenly divisible by any number other than 1 or itself. So if we are asked to list all the prime numbers between 1 and 10, we could determine the answer by considering each number between 1 and 10, and determining whether it has any factors other than 1 and itself.

Essentially, any number that has an entry in the 'Other Factors' column is not a prime factor. So the prime numbers between 1 and 10 are 1, 2, 3, 5 and 7.

(Fun Fact: Did you know that '2' is the only even prime number?)

Examples

Picking Prime Numbers

Which of the whole numbers

23, 25, 27\text{ and }29

are prime numbers?

The factors of

23

are

1\text{ and }23

. Therefore

23

is a prime number.

The factors of

25

are

1, 5\text{ and }25

. Therefore

25

is not a prime number.

The factors of

27

are

1, 3, 9\text{ and }27

. Therefore

27

is not a prime number.

The factors of

29

are

1\text{ and }29

. Therefore

29

is a prime number.

Listing Prime Numbers

List prime numbers between

5

and

12

5, 7\text{ and }11

are the prime numbers between

5

and

12

Picking Prime Numbers

Which of the whole numbers

35, 37, 39\text{ and }41

are prime numbers?

The factors of

35

are

1, 5, 7\text{ and }35

. Therefore

35

is not a prime number.

The factors of

37

are

1\text{ and }37

. Therefore

37

is a prime number.

The factors of

39

are

1, 3, 13\text{ and }39

. Therefore

39

is not a prime number.

The factors of

41

are

1\text{ and }41

. Therefore

41

is a prime number.

Listing Prime Numbers

List prime numbers between

20

and

30

23\text{ and }29

are the prime numbers between

20

and

30

Picking Prime Numbers

Which of the whole numbers

35, 41, 47\text{ and }49

are prime numbers?

The factors of

35

are

1, 5, 7\text{ and }35

. Therefore

35

is not a prime number.

The factors of

41

are

1\text{ and }41

. Therefore

41

is a prime number.

The factors of

47

are

1\text{ and }47

. Therefore

47

is a prime number.

The factors of

49

are

1, 7\text{ and }49

. Therefore

49

is not a prime number.