Properties of Factors (2024)

Consider the following multiple facts.

1 ⨯ 3 =3
1 ⨯ 6 = 6
1 ⨯ 18 =18
1 ⨯ 21 = 21
1 ⨯ 56 = 56

From the above examples we can say that:

Property 1: 1 is a factor of every number.

Property 2: Every number is the factor of itself.

Let us list the factors of following numbers.

2: 1 and 2

3: 1 and 3

4: 1, 2, and 4

5: 1 and 5

6: 1, 2, 3 and 6

Think of more factors for above numbers. There are no other factors of the numbers above.

Property 3: A number has a limited number of factors.

From the above example, we also find that

Property 4: Factor of a number is either equal to or smaller than the number.

Property 5: Biggest factor of a number is the number itself.

A number can be split into its factors. Diagrams that show the factors of a number are called factor trees.

Here is the factor tree for 4, 8, 16, 64.

Try making another factor tree for numeral 64.

Numeral 1 is the factor of all the numbers, so it has not been mentioned in the factor trees above.

A. State whether true or false.

1. Factors and multiples are same for the given number.

2. 1 is the factor of every number.

3. Every number is not the factor of itself.

4. Factors are limited.

5. Factor of a number are always smaller than the given number.

6. Factors of 16 are 2 and 4 only.

B. Fill in the blanks.

1. 7 ⨯ 6 = 42
_____ and _____ are factors of 42. 42 is the_____of 6 and 7.

2. 6 ⨯ 7 = 42
42 is the_____of 6 and 7. 6 and 7 are_____of 42.

C. Find all the factors of the following numbers.

D. Make two factor trees for each of the following numbers.

Remember: Prime numbers are numbers that have only two factors i.e., 1 and the number itself.

Example 3:

2 = 1, 2
3 = 1, 3
5 = 1, 5
7 = 1, 7
11 = 1, 11

These numbers cannot be factorised further. Such numbers are called prime numbers.

Now let us consider following numbers and their factors.

4 = 1, 2, 4

6 = 1, 2, 3, 6

8 = 1, 2, 4, 8

9 = 1, 3, 9

10 = 1, 2, 5, 10

12 = 1, 2, 3, 4, 6, 12

15 = 1, 3, 5, 15

16 = 1, 2, 4, 8, 16

Numbers above have more than two factors. These numbers are known as composite numbers.

Eratosthenes, a Greek mathematician, discovered the method of finding prime numbers. This method is known as ‘Sieve of Eratosthenes’.

Let use this method to find all the prime numbers between and 1 and 50.

Step 1: Leave number 1.

Step 2: Circle prime number 2 and cross out all the multiples of number 2.Like 4, 6, 8.....

Step 3: Circle next prime number 3 and cross out all the multiples of number 3. Like 6, 9, 12.....

Step 4: Circle next prime number 5 and cross out all the multiples of number 5. Like 10, 15, 20...

Step 5: Circle next prime number 7 and cross out all the multiples of number 7. Like 14, 21, 28...

Step 6: Circle next prime number 11 and cross out all the multiples of number 11. Like 22, 33, 44.

Step 7:Circle next prime number 13 and cross out all the multiples of number 13. Like 26, 39.

Step 8: Circle next prime number 17 and cross out all the multiples of number 17 i.e. 34.

Step 9: Circle next prime number 19 and cross out all the multiples of number 19 i.e. 38.

Using the above method, we have removed all the numbers that are not prime from the grid. Numbers that are left in the table are prime numbers less than 50.

Prime numbers less than 50: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47.