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Factors

Factors of 45 | Prime Factorization of 45 | Factor Tree of 45

Written by Prerit Jain

Updated on: 12 Aug 2023

Contents

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Factors of 45 | Prime Factorization of 45 | Factor Tree of 45

Factors of 45 | Prime Factorization of 45 | Factor Tree of 45

Factors of 45: 45 has a total of 6 factors. Factors of 45 are 1, 3, 5, 9, 15, and 45.

Factors are a set of numbers, which can divide a given number evenly. They do not leave behind reminders.

The factors of a number can be positive and negative. They can also occur in pair format. When one number is multiplied by another within the pair, the product equals the given number (45 in this case).

In this article, we will examine how to find factors of 45, its prime factorization, and factor trees with solved examples.

What Are the Factors of 45?

The factors of a number can be both positive and negative. Hence, the number 45 has both positive and negative factors.

Factors of 45: 1, 3, 5, 9, 15 and 45
Negative Factors of 45: –1, -3, -5, -9, -15 and -45
Prime Factorization of 45: 3 X 3 X 5 or 32 X 5
Pair Factors of 45: (1, 35); (3, 15) and (5, 9)
Prime Factors of 45: 3, 5
Sum of Factors of 45: 78
Sum of Prime Factors of 45: 3, 5
Factors of 45

 

What Are the Factors of 45 in Pairs?

A pair factor of 45 is a combination of two numbers, which when multiplied together gives 45 as the product. These pair factors are also written in positive and negative pairs as shown below:

Positive Pair Factors of 45

The positive pair factors of 45 are (1, 45), (3, 15), and (5, 9).

Positive Pair Factors of 45

 

Negative Pair Factors of 45

The negative pair factors of 45 are (-1, -45); (-3, -15), and (-5, -9).

Negative Pair Factors of 45

How To Find Factors of 45 Through Division Method?

We are going to use the division method to determine the factors of 45. We will, first, multiply a sequence of natural integers by 45. The numbers that divide the 45 completely without leaving remainders are the factors of 45. The following are the detailed steps for finding factors of 45 using the division method:

45 ÷ 1 = 45

45 ÷ 3 = 15

45 ÷ 5 = 9

45 ÷ 9 = 5

45 ÷ 15 = 3

45 ÷ 45 = 1

Therefore, we can see that 1, 3, 5, 9, 15, and 45 are the numbers that do not leave any remainder when divided by 45.

What Is the Prime Factorisation of 45?

We can also use prime factorization to find the factors of 45. First, we much check to see if the given number is prime or composite. If it is a prime number, it has only two factors: 1 and 45. If not, it has more than two factors.

45 is the composite number. So, it has more than 2 factors. So, we can apply the prime factorization method to find the factors of 45. It can be done by following the steps given below.

Step 1: Take the smallest prime number that can divide by 45. That number is 3.
45 ÷ 3 = 15
Step 2: The quotient we got is 15. Let us now try to divide 15 with the smallest prime number that can be divided by it. This is 3.
15 ÷ 3 = 5
Step 3:  Now we got 5 as the quotient. Dividing 5 with 5 gives us 1.
5 ÷ 5 = 1

The quotient is 1. Since 1 cannot be divided further, the prime factors of 45 are 3 X 3 X 5 or 32 X 5. We can also write it down as 3 and 5, as both of them are prime numbers.

Image representation of the prime factorization of 45:

Prime Factorization of 45

What is the Factor Tree of 45?

We can also make use of the factor tree to find the prime factors of 45. In this method, we will first place 45 at the top of the factor tree. We will write down any set of pair factors of 45. Now, again, we will further split the pair of factors. This process will go on until the branches become prime numbers. Now, circling all the prime numbers will give us the prime factors of 45.

Step 1: Let’s place the number 45 at the top of the factor tree and write down 45 in pairs, that is, 5 and 9.

Step 2: Since 5 is a prime number, we can no longer separate it. We will now divide 9 into 3 and 3. We can see that 3 is a prime number. The branches in the factor tree will now be all the prime numbers.

Hence, circling all the branches, 32 X 5 or 3 X 3 X 5 = 45, which are 45 prime factors.

Below is an image representation of the factor tree of 45, choosing 5 and 9 as pair factors of 45.

Factor tree of 45

 

Solved Examples of Factors of 45

Here are some solved examples of 45 factors:

What is the sum of all the factors of 45?
1, 3, 5, 9, 15, and 45 are the 45 factors.
1 + 3 + 5 + 9 + 15 + 45  = 78
Hence, 45 is the sum of all 78 factors.

What are the factors and prime factors of 45?
The factors of 45 are 1, 3, 5, 9, 15, and 45.
The prime factors of 45 are 5 X 32 or 3 X 3 X 5.

What’s the highest common factor between 45 and 75?
The factors of 45 are 1, 3, 5, 9, 15, and 45.
Factors of 75 are 1, 3, 5, 15, 25, and 75.
Hence, from the above, the common factors of 45 and 75 are 1, 3, 5, and 15.
The highest common factor between 45 and 75 is 15.

What’s the highest common factor between 45 and 60?
The factors of 45 are 1, 3, 5, 9, 15, and 45.
Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
Hence, from the above, the common factors of 45 and 60 are 1, 2, 3, 5, and 15.
The highest common factor between 45 and 60 is 15.

Is 15 a factor of 45?
Yes, 15 is a factor of 45.
As 45 ÷ 3 = 15.

What are the factors of -45?
The factors of -45 are -1, -3, -5, -9, -15, and -45.

What are the common factors of 45 and 100?
To find the common factors of 45 and 100, we need to find the factors of both numbers.
Factors of 45: 1, 3, 5, 9, 15 and 45
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50 and 100
Hence the common factors of 45 and 100 are 1 and 5.

What are all the factors of 45?
The factors of 45 are 1, 3, 5, 9, 15, and 45.

What are the factors of 45 that are composite?
Any number which has more than 2 factors is known as a composite number.
The list of number which has more than 2 factors in factors of 45 is 9, 15, and 45.

What factors of 45 are multiples of 5?
The factors of 45 that are multiples of 5 are 5, 15, and 45.
5 x 1 = 5
5 x 3 = 15
5 x 9 = 45.

How many 45 factors are odd?
All factors of 45 are odd numbers and they are 1, 3, 5, 9, 15, and 45.

What are the factors of 45 and 72?
The factors of 45 are 1, 3, 5, 9, 15, and 45.
The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72.

What are the common factors of 45 and 150?
To list out the common factors of 45 and 150, we need to find the factors of both numbers.
Factors of 45: 1, 3, 5, 9, 15 and 45
Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75 and 150
From the above, the common factors of 45 and 150 are 1, 3, 5 and 15.

How many different factors are there for the number 45?
A total of 6 factors are there for the number 45 and they are 1, 3, 5, 9, 15, and 45.

How many pair factors are there in 45?
A total of 3 pairs are there in factors of 45.

What is the largest factor of 45?
The largest factor of 45 is 45.
The second largest factor of 45 is 15.

FAQs on Factors of 45

List all the factors of 45
1, 3, 5, 9, 15, and 45 are the 45 factors.

What are the composite factors of 45?
9, 15, and 45 are the 45 composite factors. Composite factors are those that have more than 2 factors other than 1 and itself.

What are the factors of 45 in pairs?
(1, 45), (3, 15), and (5, 9) are the 45 factors of pairs.

What are the positive factors for 45?
1, 3, 5, 9, 15, and 45 are the positive factors for 45.

List the prime factors of 45.
The prime factor of 45 is 32 X 5 or 3 X 3 X 5.

We now have all the necessary facts about the factors of 45. We hope that this blog has been informational and simple to understand.

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Prerit Jain

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