[Maths Class Notes] on Factors of 90 Pdf for Exam

Factors of a number are the product of such numbers which completely divide the given number. Factors of a given number can be either positive or negative numbers. By multiplying the factors of a number, we get any given number. Let’s take an example: 1, 2, 3, and 6 are the factors of 6. On multiplying two or more numbers, we get 6. Hence, we have 2 x 3 = 6 or 1 x 6 = 6. In this session, we will study the factors of 36 definitions, how to find the factors of 36, and examples. Let’s discuss the factors of 90.

What are the Factors?

Factors can be defined as the numbers you multiply to get another number. There are many numbers that have more than one factorization (it means that they can be factored in more than one way). For instance, the number 12 can be factored as 1×12 or 2×6 or 3×4. 

Here’s what a prime factor is!

A number that can only be factored 1 time is known as a prime number.

Factors of 90 Definition

The factors of a number are defined as the numbers which, when multiplied, will give the original number; by multiplying the two factors we get the result as the original number. The factors of any number can be either positive or negative integers.

Factors of 90 are all the integers that can evenly divide the given number, 90.

Now, let us find all factors of 90.

What are the Factors of 90 (Prime Factorization of 90)?

Let’s find out what are the factors of 90. According to the definition of factors of 90, we know that all factors of 90 are all the positive or negative integers that divide the number 90 completely. So, let us simply divide the number 90 by every number which completely divides 90 in ascending order till 90.

90 ÷ 1 = 90

90 ÷ 2 = 45

90 ÷ 3 = 30

90 ÷ 5 = 18

90 ÷ 6 = 15

90 ÷ 9 = 10

90 ÷ 10 = 9

90 ÷ 15 = 6

90 ÷ 18 = 5

90 ÷ 30 = 3

90 ÷ 45 = 2

90 ÷ 90 = 1

So, the factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.

We know that factors also include negative integers. Hence, we can also have a list of negative factors of 90, which are -1, -2, -3, -5, -6, -9, -10, -15, -18, -30, -45, and -90.

What are the factors of 90? 

Prime Factorization of 90:

90 = 1(90

= 2(45)

= 3(30)

=  5(18)

= 6(15) 

= 9(10)

Factors of 90 can be Listed as Follows:

Hence, 90 has a total of 10 positive factors and 10 negative factors.

Pair Factors of 90 (Prime Factorization of 90)

Let’s know the pair factors of 90.

Factor Pairs of 90 are combinations of two factors that, when multiplied together, give 90.

List of all the Positive Factor Pairs of 90:

1 x 90 = 90

2 x 45 = 90

3 x 30 = 90

5 x 18 = 90 

6 x 15 = 90 

9 x 10 = 90 

10 x 9 = 90 

15 x 6 = 90 

18 x 5 = 90 

30 x 3 = 90 

45 x 2 = 90 

90 x 1 = 90 

As we know, all factors of 90 include negative integers too. 

List of all the Negative Factor Pairs of 90:

-1 x- 90 = 90

-2 x -45 = 90

-3 x-30 = 90

-5 x -18 = 90 

-6 x -15 = 90 

-9 x -10 = 90 

-10 x- 9 = 90 

-15 x- 6 = 90 

-18 x -5 = 90 

-30 x -3 = 90 

-45 x- 2 = 90 

-90 x -1 = 90 

Prime Factorization of 90

According to the prime factor definition, we know that the prime factor of a number is the product of all the factors that are prime (a number that divides by itself and only one). Hence, we can list the prime factors from the list of factors of 90.

The other way to find the prime factorization of 90 is by prime factorization or by factor tree.

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What do Factors of 90 Add up to?

We know all the factors of 90, so the factors of 90 add up to:

Prime factors – 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90

Therefore, the factors of 90 add up to 234.

Prime Factor of any Prime Number

For example, let’s find the prime factor of 41.

To make the task easier, we can find the square root of the given number. Let’s suppose that 41 is not a prime number. Then, the number would be divisible by at least one prime number which is less than or equal to the square root of the number √41 ≈ 6.4. Now, list all the prime numbers less than 6, which are 2, 3, and 5, and since 41 cannot be divided evenly by 2, 3, or 5, we can conclude that 41 is a prime number. So, there are no prime factors of 41.

Solved Examples

Example 1: Write down the factors of 48.

Solution:

48 ÷ 1 = 48

48 ÷ 2 = 24

48 ÷ 3 = 16

48 ÷ 4 = 12

48 ÷ 6 = 8

48 ÷ 8 = 6

48 ÷ 12= 4

48 ÷ 16 = 3

48 ÷ 24 = 2

48 ÷ 48 = 1

Therefore, the factors of 16 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

Example 2: Write down the factors of 68.

Solution:

68 ÷ 1 = 68

68 ÷ 2 = 34

68 ÷ 4 = 17

68 ÷ 17 = 4

68 ÷ 34 = 2

68 ÷ 68 = 1

Therefore, the factors of 16 are 1, 2, 4, 17, 34, and 68.