Factors

# Factors of 90 | Prime Factorization of 90 | Factor Tree of 90

Written by Prerit Jain

Updated on: 24 Aug 2023

## Factors of 90

Calculate Factors of

The Factors are

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## What are the factors of 90

Factors are numbers that can be evenly divided into the given number. For example, the factors of 10 are 1, 2, 5, and 10, because these are the numbers that can be divided into 10 without any leftover parts.

To find the factors of a number, you can start by dividing the number by the smallest number, which is 1. If the number can be divided by 1 with no leftover parts, then 1 is a factor of the number. Then, you can try dividing the number by the next smallest number, which is 2. If the number can be divided by 2 with no leftover parts, then 2 is a factor of the number. You can continue this process with the next smallest number until you reach the number itself. If the number can be divided by itself with no leftover parts, then it is also a factor of the number.

To find the factors of 90, you can start by dividing 90 by 1. 90 divided by 1 is 90 with no leftover parts, so 1 is a factor of 90. Then, you can divide 90 by 2. 90 divided by 2 is 45 with no leftover parts, so 2 is a factor of 90. You can then divide 90 by 3. 90 divided by 3 is 30 with no leftover parts, so 3 is a factor of 90. You can continue this process until you reach 90. When you divide 90 by 90, you get 1 with no leftover parts, so 90 is a factor of 90.

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

## How to Find Factors of 90

To find the factors of 90, you can use one of the following methods:

Here are four methods that you can use to find the factors of 90:

1. Factors of 90 using the Multiplication Method
2. Factors of 90 using the Division Method
3. Prime Factorization of 90
4. Factor tree of 90

## Factors of 90 Using the Multiplication Method

The multiplication method is a way to find the factors of a number by trying different pairs of numbers that can be multiplied together to get the number. To use the multiplication method to find the factors of 90, you can start by trying to multiply different pairs of numbers together to see if you can get 90. You might try 1 and 90, 2 and 45, or 5 and 18. When you multiply 1 and 90 together, you get 90, so 1 and 90 are both factors of 90. When you multiply 2 and 45 together, you also get 90, so 2 and 45 are both factors of 90. When you multiply 5 and 18 together, you also get 90, so 5 and 18 are both factors of 90.

Using the multiplication method, you can find the factors of 90 by trying different pairs of numbers and seeing which ones multiply together to get 90. Some of the pairs of numbers that work are 1 and 90, 2 and 45, and 5 and 18. These pairs of numbers are called the factors of 90.

## Factors of 90 Using the Division Method

To use the division method to find the factors of a number, you need to start by dividing the number by the smallest number, which is 1. If the number can be divided by 1 with no leftover parts, then 1 is a factor of the number. Then, you can try dividing the number by the next smallest number, which is 2. If the number can be divided by 2 with no leftover parts, then 2 is a factor of the number. You can continue this process with the next smallest number until you reach the number itself. If the number can be divided by itself with no leftover parts, then it is also a factor of the number.

To find the factors of 90 using the division method, you can start by dividing 90 by 1. 90 divided by 1 is 90 with no leftover parts, so 1 is a factor of 90. Then, you can divide 90 by 2. 90 divided by 2 is 45 with no leftover parts, so 2 is a factor of 90. You can then divide 90 by 3. 90 divided by 3 is 30 with no leftover parts, so 3 is a factor of 90. You can continue this process until you reach 90. When you divide 90 by 90, you get 1 with no leftover parts, so 90 is a factor of 90.

Therefore, the factors of 90 using the division method are 1, 2, 3, 5, 9, 10, 15, 18, 30, 45, and 90.

## Prime Factorization of 90

Calculate Prime Factors of

The Prime Factors of 90 =

2 x

3 x

3 x

5

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Prime factorization is a way to express a number as the product of its prime factors. A prime factor is a factor of a number that is itself a prime number. For example, the prime factors of 15 are 3 and 5, because 3 and 5 are both prime numbers and they are also both factors of 15.

To find the prime factorization of a number, you can start by dividing the number by the smallest prime number, which is 2. If the number can be evenly divided by 2, then 2 is a prime factor of the number. If the number cannot be evenly divided by 2, then you can try dividing it by the next smallest prime number, which is 3. If the number can be evenly divided by 3, then 3 is a prime factor of the number. You can continue this process with the next smallest prime number until you reach the number itself.

To find the prime factorization of 90, you can start by dividing 90 by 2. 90 divided by 2 is 45 with no leftover parts, so 2 is a prime factor of 90. You can then divide 45 by 2. 45 divided by 2 is 22 with no leftover parts, so 2 is a prime factor of 90. You can continue this process until you reach a number that cannot be evenly divided by 2. When you divide 9 by 2, you get 4 with a leftover part of 1, so 2 is not a factor of 9. However, 9 is a prime number, so it is a prime factor of 90.

Therefore, the prime factorization of 90 is 2 x 2 x 3 x 3 x 5, or 2^2 x 3^2 x 5.

## Factor tree of 90

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A factor tree is a way to find the factors of a number by breaking the number down into smaller numbers until you reach the prime factors. Prime factors are factors of a number that are themselves prime numbers.

To use a factor tree to find the factors of a number, you can start by writing the number at the top of the tree. Then, you can divide the number by the smallest number that goes into it evenly, with no leftover parts. For example, if you want to find the factors of 90, you can start by dividing 90 by 2. 90 divided by 2 is 45 with no leftover parts, so 2 is a factor of 90. You can then write 2 and 45 on the tree, with 45 below 2.

Next, you can divide 45 by the smallest number that goes into it evenly, with no leftover parts. In this case, the smallest number that goes into 45 evenly is 3. 45 divided by 3 is 15 with no leftover parts, so 3 is a factor of 90. You can then write 3 and 15 on the tree, with 15 below 3.

You can continue this process until you reach the prime factors of the number. The prime factors of 90 are 2, 3, and 5. You can write these prime factors on the tree, with no numbers below them.

Using a factor tree, you can find the factors of 90 by dividing the number by different numbers and seeing which ones go into the number evenly, with no leftover parts. The factor tree for 90 shows the different pairs of numbers that can be multiplied together to get 90. The prime factorization of 90 is the product

## Factor Pairs of 90

Calculate Pair Factors of

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

So Pair Factors of 90 are

(1,90)

(2,45)

(3,30)

(5,18)

(6,15)

(9,10)

(10,9)

(15,6)

(18,5)

(30,3)

(45,2)

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To find the factor pairs of 90, you can follow these steps:

• Begin by writing down the number 90.
• Write down the factors of 90 in pairs, such that the product of each pair is equal to 90. For example, you can write down the pairs (1, 90), (2, 45), etc.
• Determine the factor pairs of 90 by multiplying the numbers in each pair. The factor pairs of 90 are (1, 90), (2, 45), (3,30), (5,18), (10,9), (15,6).

This method involves writing down the factors of 90 in pairs and then finding the factor pairs by multiplying the numbers in each pair.

## Factors of 90 – Quick Recap

• Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90.
• Negative Factors of 90: -1, -2, -3, -5, -6, -9, -10, -15, -18, -30, -45, and -90.
• Prime Factors of 90: 2 × 3 × 3 × 5
• Prime Factorization of 90: 2 × 3 × 3 × 5

## Factors of 90 – Fun Facts

• The factors of 90 are the numbers that can be multiplied together to produce 90. The factors of 90 are 1, 2, 4, and 90.
• The number 90 is a perfect cube, which means that it can be written as the product of three equal integers. In this case, the three equal integers are 2 x 2 x 2, or 2^3.
• The number 90 is also a perfect power of 2. This means that it can be written as the product of two equal integers, with one of the integers being 2. In this case, the two equal integers are 2 x 2, or 2^2.
• The number 90 is considered to be a lucky number in some cultures, as it is considered to be a symbol of abundance and prosperity.

Also Check: Multiples, Square Root, and LCM

## Solved Examples of Factor of 90

Q.1: List all the pairs of factors for 90 in increasing order
Solution
: The pairs of factors for 90 in increasing order are (1,90), (2,45), (3,30) and (5,18).

Q.2: What is the smallest number that can go into 90?
Solution:
The smallest number that can go into 90 is 1 since any number divided by 1 will remain unchanged.

Q.3: How many even factors does 90 have?
Solution:
The factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90. Out of these factors, the even numbers are 2, 6, 10, 18, 30, and 90. There are six even factors of 90.

Q.4: What is the greatest common factor for 88 and 96?
Solution: The greatest common factor for 88 and 96 is 8 since it is the highest number that can be evenly divided into both numbers without a remainder ​(​no shared divisors)​ .

Q.5: Is there any perfect square within the range of numerators from 85 to 91?   Solution: No, there is no perfect square within this range.

Q.6: Does 87 have any cube factors? If so name them…
Solution: No, 87 does not have any cube factors. The prime factorization of 87 is 3 x 29, and none of these prime factors are cubes.

Q.7: What would be the least common multiple between 85 and 95?
Solution: The least common multiple between 85 and 95 is 1615.

Q.8: Find the prime factorization of 98.
Solution: The prime factorization of 98 is 2 x 7 x 7; since 2 x 7 x 7 = 98

## Frequently Asked Questions on Factors of 90

### What is the highest common factor for 90 and 60?

The highest common factor for 90 and 60 is 30; since it is the highest number that can be divided into both numbers without a remainder (no shared divisors).

### How many prime factors does 90 have?

There are three prime factors of 90; 2, 3 and 5.

### Is there any perfect square number within the range of numerators from 85 to 91?

No, there is no perfect square within this range.

### Does 84 have any cube factors? If so, name them…

No, 87 does not have any cube factors. The prime factorization of 87 is 3 x 29, and none of these prime factors are cubes.

### What would be the least common multiple between 86 and 94?

The least common multiple between 86 and 94 is 2164.

### Find the prime factorization of 98.

The prime factorization of 98 is 2 x 7 x 7; since 2 x 7 x 7 = 98.

### Is there any pair of factors for 87 in increasing order?

Yes, there is one pair of factors for 87; (1,87).

### What is the smallest number that can go into 88?

The smallest number that can go into 88 is 1 since any number divided by 1 will remain unchanged.

Written by by

Prerit Jain

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