# Factors of 90

Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90

#### How to find factors of a number

 1.   Find factors of 90 using Division Method 2.   Find factors of 90 using Prime Factorization 3.   Find factors of 90 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 90

• Divide 90 by 1: 90 ÷ 1 : Remainder = 0
• Divide 90 by 2: 90 ÷ 2 : Remainder = 0
• Divide 90 by 3: 90 ÷ 3 : Remainder = 0
• Divide 90 by 5: 90 ÷ 5 : Remainder = 0
• Divide 90 by 6: 90 ÷ 6 : Remainder = 0
• Divide 90 by 9: 90 ÷ 9 : Remainder = 0
• Divide 90 by 10: 90 ÷ 10 : Remainder = 0
• Divide 90 by 15: 90 ÷ 15 : Remainder = 0
• Divide 90 by 18: 90 ÷ 18 : Remainder = 0
• Divide 90 by 30: 90 ÷ 30 : Remainder = 0
• Divide 90 by 45: 90 ÷ 45 : Remainder = 0
• Divide 90 by 90: 90 ÷ 90 : Remainder = 0

Hence, Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90

#### 2. Steps to find factors of 90 using Prime Factorization

A prime number is a number that has exactly two factors, 1 and the number itself. Prime factorization of a number means breaking down of the number into the form of products of its prime factors.

There are two different methods that can be used for the prime factorization.

#### Method 1: Division Method

To find the primefactors of 90 using the division method, follow these steps:

• Step 1. Start dividing 90 by the smallest prime number, i.e., 2, 3, 5, and so on. Find the smallest prime factor of the number.
• Step 2. After finding the smallest prime factor of the number 90, which is 2. Divide 90 by 2 to obtain the quotient (45).
90 ÷ 2 = 45
• Step 3. Repeat step 1 with the obtained quotient (45).
45 ÷ 3 = 15
15 ÷ 3 = 5
5 ÷ 5 = 1

So, the prime factorization of 90 is, 90 = 2 x 3 x 3 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 90 as shown below:

So, the prime factorization of 90 is, 90 = 2 x 3 x 3 x 5.

#### 3. Find factors of 90 in Pairs

Pair factors of a number are any two numbers which, which on multiplying together, give that number as a result. The pair factors of 90 would be the two numbers which, when multiplied, give 90 as the result.

The following table represents the calculation of factors of 90 in pairs:

Factor Pair Pair Factorization
1 and 90 1 x 90 = 90
2 and 45 2 x 45 = 90
3 and 30 3 x 30 = 90
5 and 18 5 x 18 = 90
6 and 15 6 x 15 = 90
9 and 10 9 x 10 = 90

Since the product of two negative numbers gives a positive number, the product of the negative values of both the numbers in a pair factor will also give 90. They are called negative pair factors.

Hence, the negative pairs of 90 would be ( -1 , -90 ) , ( -2 , -45 ) , ( -3 , -30 ) , ( -5 , -18 ) , ( -6 , -15 ) and ( -9 , -10 ) .

#### What are factors?

In mathematics, a factor is that number which divides into another number exactly, without leaving a remainder. A factor of a number can be positive or negative.

#### Properties of factors

• Each number is a factor of itself. Eg. 90 is a factor of itself.
• Every number other than 1 has at least two factors, namely the number itself and 1.
• Every factor of a number is an exact divisor of that number, example 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 are exact divisors of 90.
• 1 is a factor of every number. Eg. 1 is a factor of 90.
• Every number is a factor of zero (0), since 90 x 0 = 0.

• Which is the smallest prime factor of 90?

Smallest prime factor of 90 is 2.

• Is 90 a perfect square?

No 90 is not a perfect square.

• What are five multiples of 90?

First five multiples of 90 are 180, 270, 360, 450, 540.

• What is prime factorization of 90?

Prime factorization of 90 is 2 x 3 x 3 x 5.

• What are factors of 90?

Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.

• How do you find factors of a negative number? ( eg. -90 )?

Factors of -90 are -1, -2, -3, -5, -6, -9, -10, -15, -18, -30, -45, -90.

• Is 90 a whole number?

Yes 90 is a whole number.

• Which is greatest factor of 90?

The greatest factor of 90 is 45.

• What are the prime factors of 90?

The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.
Prime factors of 90 are 2, 3, 3, 5.

#### Examples of Factors

Ariel has been assigned the task to find the product of all the prime factors of 90. Can you help her?

Prime factors of 90 are 2, 3, 3, 5.
Hence, the product of prime factors of 30.

Can you help Rubel to find out the product of the even factors of 90?

Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.
Even factors of 90 are 2, 6, 10, 18, 30, 90.
Hence, product of even factors of 90 is; 2 x 6 x 10 x 18 x 30 x 90 = 5832000.

Joy wants to calculate mean of all the factors of 90. Help him in finding the mean of 90.

Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.
To calculate the mean we need to calculate the sum of factors first. Sum of factors of 90 is 1 + 2 + 3 + 5 + 6 + 9 + 10 + 15 + 18 + 30 + 45 + 90 = 234.
Hence, the mean of factors of 90 is 234 ÷ 12 = 19.50.

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 90? Help her in writing all the factors.

Positive factors are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.
Negative factors are -1, -2, -3, -5, -6, -9, -10, -15, -18, -30, -45, -90.

How many factors are there for 90?

Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90.
So there are in total 12 factors.

Joey wants to write all the prime factors of 90 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 90 are 2, 3, 3, 5.
So in exponential form it can be written as 2 x 32 x 5.

Kevin has been asked to write 11 factor(s) of 90. Can you predict the answer?

11 factor(s) of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45.