Factors of 90

Factors of 90 include 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90. Factors of a number are the numbers that can divide the original number without leaving any remainder. Factors include both positive and negative integers.

In this article, we will discuss all the topics related to the factors of 90, including all the factors of 90, prime factors of 90, and methods to find these factors.

What are Factors?

Factors of a number can be defined as the numbers which divide the number exactly without leaving any number.

In the case of 90, all the numbers like 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90 are the factors of 90 because they all divide 90 completely without leaving any remainder.

Some other examples of Factors of a number include:

• Factors of 53 = 1, and 53
• Factors of 27 = 1, 3, 9, and 27.

Properties of Factors

These are some of the key properties of the factors of a number:

• Zero cannot be a factor of any number as division by 0 is not defined.
• 1 is a factor of every number.
• Every number other than 1 has at least two factors, 1 and the number itself.
• A factor of a number is always smaller than or equal to the number.
• A factor of a number can never be a decimal or a fraction.
• Every prime number has only two factors, 1 and the number itself.

Read More, Factors of a number.

What are Factors of 90?

Factors of 90 are those numbers that can evenly divide 90 without leaving a remainder. Factors of 90 can also be described as numbers which when multiplied together results into 90. For Example: product of 2 and 45 results into 90, hence 2 and 45 are factors of 90.

Following is the list of factors of 90, calculated by division method.

Factor of 96	Division	Quotient
1	90 ÷ 1	90
2	90 ÷ 2	45
3	90 ÷ 3	30
5	90 ÷ 5	18
6	90 ÷ 6	15
9	90 ÷ 9	10

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

All Factors of 90

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

Prime Factors of 90

Factors of 90 include both prime and composite numbers. However, we can also express 90 as the product of only prime numbers. The prime numbers which when multiplied together gives back the original number (here 90), are called the prime factors of that number.

For 90, Prime factors are 2 x 3 x 3 x 5.

Read More, Prime Numbers

Factors of 90 Calculator

Use the below given calculator to find the factors of 90 and other integers.

How to Find Factors of 90?

Factors of 90 can also be determined by the multiplication method. In this method, we find pairs of number which when multiplied together returns back 90. List of the factors of 90 by multiplication method is given below:

• 1 × 90 = 90
• 2 x 45 = 90
• 3 x 30 = 90
• 5 x 18 = 90
• 6 x 15 = 90
• 9 x 10 = 90

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

Prime Factorization of 90

Prime Factorization is the other method to find the factors of 90. By this method, we can express 90 as the factor of prime numbers. Prime factorization is a process of repeated division such that the divisor each time is only a prime number. For 90,

90 ÷ 2 = 45

45 ÷ 3 = 15

15 ÷ 3 = 5

5 ÷ 5 = 1

We can see, that in each step, we have only used a prime number for division until we completely divide 90. This can be represented as follows:

Factor Tree of 90

Factor tree is a chart that shows all the prime factors of a number in the form of a tree like diagram, for 90 we can make the factor tree of 90 as follows:

Read More,

• Factors of 96
• Factors of 16
• Factors of 72

Factor Pairs of 90

Factor pairs are the factors when paired together, give the original number back. For 90, the two factor whose product gives 90 is known as factor pair of 90. These pairs can include both positive and negative numbers. The following table gives an illustration of positive and negative factor pairs of 90.

Positive Factor Pairs of 90

The positive factor pairs of 90 are:

Positive Factor Pair of 90	Multiplication of Factor Pair of 90
(1, 90)	1 × 90 = 90
(2, 45)	2 × 45 = 90
(3, 30)	3 × 30 = 90
(5, 18)	5 × 18 = 90
(6, 15)	6 × 15 = 90
(9, 10)	9 × 10 = 90

Negative Factor Pairs of 90

The negative factor pairs of 90 are:

Negative Factor Pair of 90	Multiplication of Factor Pair of 90
(-1, -90)	-1 × -90 = 90
(-2, -45)	-2 × -45 = 90
(-3, -30)	-3 × -30 = 90
(-5, -18)	-5 × -18 = 90
(-6, -15)	-6 × -15 = 90
(-9, -10)	-9 × -10 = 90

Solved Examples on Factors of 90

Example 1: Find the common factors of 90 and 180.

Solution:

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

Factors of 180 = 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90 and 180

Common factors of 90 and 180 = 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90.

Example 2: Is 90 a prime number?

Solution:

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

Since 90 has more than two factors, it is not a prime number.

Example 3: Are factors and multiples of 90 the same?

Solution:

No, the factors of 90 are the numbers smaller than or equal to 90, that completely divide 90 whereas, the multiples are the numbers that come in the table of 90 and are equal to or greater than 90.

Example 4: What is the sum of the factors of 90?

Solution:

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

The sum therefore is 234.

Practice Problems on Factors of 90

Problem 1: What is the greatest prime factor of 90?

Problem 2: What is the HCF of 90 and 100.

Problem 3: What are positive pair factors of 90?

Problem 4: Find the common factors of 90 and 120. .

Problem 5: What is the product of the greatest and smallest factor of 90?

Factors of 90: Frequently Asked Questions

List all Factors of 90.

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

How do you Find the Factors of 90?

To find the factors of 90, you can divide 90 by various numbers and check which ones result in whole number quotients without remainders.

What is Prime Factorization of 90?

The prime factorization of 90 is 2 x 3 x 3 x 5.

How many Factors does 90 have?

The total factors of 90 are 12.

What are Highest and Smallest Factor of 90?

The highest and smallest factors of 90 are 90 and 1 respectively.

Is 90 a Perfect Square?

No, 90 is not a perfect square because it cannot be expressed as the square of an integer.