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Factors

# Factors of 40 | Prime Factorization of 40 | Factor Tree of 40

Written by Prerit Jain

Updated on: 18 Aug 2023

### Factors of 40 | Prime Factorization of 40 | Factor Tree of 40

Factors of 40: The number 40 has 8 factors in total and they are 1, 2, 4, 5, 8, 10, 20, and 40. Factors are a set of numbers that divide the original number evenly, without leaving a reminder. The numbers 1, 2, 4, 5, 8, 10, 20, and 40 will divide the number 40 evenly. So, they are the factors of 40.

Factors are both positive and negative. They can also be written in the pairs. Multiplying the pairs with each other can give you the number (39) as the product. In this article, we will examine how to find factors of 40, its prime factorization, and factor trees with solved examples. Continue reading to know more.

## What Are the Factors of 40 in Pairs?

A pair factor of 40 is a combination of two numbers when multiplied together giving the product 40. These pair factors are also written in positive and negative pairs as shown in the tables below:

### Positive Pair Factors of 40

The positive pair factors of 40: (1, 40); (2, 20); (4, 10), and (5, 8).

### Negative Pair Factors of 40

The negative pair factors of 40: (-1, -40); (-2, -20); (-4, -10) and (-5, -8).

## How To Find Factors of 40 Through Division Method?

Let us determine the factors of 40, using the division method. In this method, we need to multiply a sequence of natural integers by 40. The numbers that divide the 40 evenly without remainders are the factors of 40. The following are the detailed steps for finding factors of 40 using the division method:

40 ÷ 1 = 40

40 ÷ 2 = 20

40 ÷ 4 = 10

40 ÷ 5 = 8

40 ÷ 8 = 5

40 ÷ 10 = 4

40 ÷ 20 = 2

40 ÷ 40 = 1

We can see that 1, 2, 4, 5, 8, 10, 20, and 40 are the numbers that do not leave any remainder when divided by 40. Therefore, they are the factors of 40.

## What Is the Prime Factorization of 40?

Before doing the prime factorization for a number, we must check if the given number is a prime number. If it is a prime number, then it has only two factors: 1 and 40. If the number is a composite number, it has more than two factors.
40 is the composite number. So, we have more than two factors. This validates the use of the prime factorization method to find the factors of 40.
The steps to find prime factors of 40 using the prime factorization method are given below:

Step 1: Divide the number 40 with the smallest prime number that can divide it. That number is 2.
40 ÷ 2 = 20

Step 2: Divide the number 20 (quotient) by the smallest prime number. This is also 2.
20 ÷ 2 = 10

Step 3: Divide the quotient by 2 repeatedly until you get the number prime number as the quotient.
10 ÷ 2 = 5

Step 4: The quotient we get is 5. Dividing 5 with 5 gives us 1.
5 ÷ 5 = 1

The final quotient is 1. Since 1 cannot be divided further, the prime factors of 40 are 2 X 2 X 2 X 5 or 23 X 5. We can also write it down as 2 and 5, as both of them are prime numbers.

Pictorial representation of the prime factorization of 40:

## What is the Factor Tree of 40?

We can also use the factor tree to find the prime factors of 40. In this method, we will place the number 40 at the top of the factor tree. Now, as part of the branches, we will write down any set of pair factors of 40. We will again split the pair of factors. This process will continue until the branches become prime numbers. Now, circling all the prime numbers will give us the prime factors of 40.

Step 1: Let’s place the number 40 at the top of the factor tree. Next, write down 40 in pairs. For example, 5 and 8.

Step 2: Since 5 is a prime number, we can no longer separate it. We will now take 8 and divide it into 2 and 4.

Step 3: As we can see, 2 is a prime number but 4 is not, so we will split 4 into 2 and 2. The branches in the factor tree will now be all the prime numbers.

Hence, circling all the branches, 23 X 5 or 2 X 2 X 2 X 5 = 40, which are 40 prime factors.

There are many ways in which we can write the factor tree of 40. The following image is an accurate representation of the factor tree of 40. It chooses 5 and 8 as pair factors of 40.

## Solved Examples on Factors of 40

Here are some solved examples of factors of 40:

What is the sum of all the factors of 40?
1, 2, 4, 5, 8, 10, 20, and 40 are the 48 factors.
1 + 2 + 4 + 5 + 8 + 10 + 20 + 40 = 90
Hence, 90 is the sum of all 40 factors.

What are the factors and prime factors of 40?
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.
The prime factors of 40 are: 2 X 2 X 2 X 5= 23 × 5

What’s the highest common factor between 40 and 100?
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.
Factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
Hence, from the above, the common factors of 40 and 100 are 1, 2, 4, 5, 10, and 20.
The highest common factor between 40 and 100 is 20.

What’s the highest common factor between 40 and 50?
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.
Factors of 50 are 1, 2, 5, 10, 25, and 50.
Hence, from the above, the common factors of 40 and 50 are 1, 2, 5, and 10.
The highest common factor between 40 and 50 is 10.

Is 8 a factor of 40?
Yes, 8 is a factor of 40.
40 ÷ 5 = 8.

What are the factors of -40?
The factors of -40 are -1, -2, -4, -5, -8, -10, -20, and -40.

What are the common factors of 40 and 90?
To find the common factors of 40 and 90, we need to find the factors of both numbers.
Factors of 40: 1, 2, 4, 5, 8, 10, 20 and 40
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90
Hence the common factors of 40 and 90 are 1, 2, 5, and 10.

What are all the factors of 40?
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.

What are the factors of 40 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 40 is 4, 8, 10, 20, and 40.
Hence the factors of 40 that are composite are 4, 8, 10, 20, and 40.

What factors of 40 are multiples of 4?
The factors of 40 that are multiples of 4 are 4, 8, 20, and 40.
4 x 1 = 4
4 x 2 = 8
4 x 5 = 20
4 x 10 = 40.

How many factors of 40 odd?
Only one factor of 40 is an odd number and it is 1.

What are the factors of 32 and 40?
The factors of 40 are 1, 2, 4, 5, 8, 10, 20 and 40
The factors of 32 are 1, 2, 4, 8, 16, 32, and 64

What are the common factors of 40 and 48?
To list out the common factors of 40 and 48, we need to find the factors of both 40 and 48.
Factors of 40: 1, 2, 4, 5, 8, 10, 20 and 40
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48
From the above, the common factors of 40 and 48 are 1, 2, and 4.

How many different factors are there for the number 40?
A total of 8 factors are there for the number 40 and they are 1, 2, 4, 5, 8, 10, 20, and 40.

What factors of 40 are multiples of 2?
The factors of 40 that are multiples of 2 are 2, 4, 8, 10, 20, and 40.

How many pair factors are there in 40?
A total of 4 pairs are there in factors of 40.

What is the largest factor of 40?
The largest factor of 40 is 40.
The second largest factor of 40 is 20.

## FAQs on Factors of 40

List all the factors of 40
1, 2, 4, 5, 8, 10, 20, and 40 are the 40 factors.

What are the composite factors of 40?
4, 8, 10, 20, and 40 are the composite factors of 40. Composite factors are those that have more than 2 factors other than 1 and itself.

What are the factors of 40 in pairs?
(1, 40), (2, 20), (4, 10), and (5, 8) are the 40 factors of pairs.

What are the positive factors for 40?
1, 2, 4, 5, 8, 10, 20, and 40 are the positive factors for 40.

What are the largest and second-largest factors of 40?
The largest factor of 40 is 40. The second largest factor of 40 is 20.

We now have all the necessary information on the factors of 40.

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Written by

Prerit Jain

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