# Factors of 40

Factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40

#### How to find factors of a number

 1.   Find factors of 40 using Division Method 2.   Find factors of 40 using Prime Factorization 3.   Find factors of 40 in Pairs 4.   How can factors be defined? 5.   Frequently asked questions 6.   Examples of factors

### Example: Find factors of 40

• Divide 40 by 1: 40 ÷ 1 : Remainder = 0
• Divide 40 by 2: 40 ÷ 2 : Remainder = 0
• Divide 40 by 4: 40 ÷ 4 : Remainder = 0
• Divide 40 by 5: 40 ÷ 5 : Remainder = 0
• Divide 40 by 8: 40 ÷ 8 : Remainder = 0
• Divide 40 by 10: 40 ÷ 10 : Remainder = 0
• Divide 40 by 20: 40 ÷ 20 : Remainder = 0
• Divide 40 by 40: 40 ÷ 40 : Remainder = 0

Hence, Factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40

#### 2. Steps to find factors of 40 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 40 using the division method, follow these steps:

• Step 1. Start dividing 40 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 40, which is 2. Divide 40 by 2 to obtain the quotient (20).
40 ÷ 2 = 20
• Step 3. Repeat step 1 with the obtained quotient (20).
20 ÷ 2 = 10
10 ÷ 2 = 5
5 ÷ 5 = 1

So, the prime factorization of 40 is, 40 = 2 x 2 x 2 x 5.

#### Method 2: Factor Tree Method

We can follow the same procedure using the factor tree of 40 as shown below:

So, the prime factorization of 40 is, 40 = 2 x 2 x 2 x 5.

#### 3. Find factors of 40 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 40 would be the two numbers which, when multiplied, give 40 as the result.

The following table represents the calculation of factors of 40 in pairs:

Factor Pair Pair Factorization
1 and 40 1 x 40 = 40
2 and 20 2 x 20 = 40
4 and 10 4 x 10 = 40
5 and 8 5 x 8 = 40

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 40. They are called negative pair factors.

Hence, the negative pairs of 40 would be ( -1 , -40 ) , ( -2 , -20 ) , ( -4 , -10 ) and ( -5 , -8 ) .

#### 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. 40 is a factor of itself.
• 1 is a factor of every number. Eg. 1 is a factor of 40.
• Every number is a factor of zero (0), since 40 x 0 = 0.
• 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, 4, 5, 8, 10, 20, 40 are exact divisors of 40.
• Factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. Each factor divides 40 without leaving a remainder.
• Every factor of a number is less than or equal to the number, eg. 1, 2, 4, 5, 8, 10, 20, 40 are all less than or equal to 40.

• Is 40 a perfect square?

No 40 is not a perfect square.

• What are factors of 40?

Factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40.

• Which is greatest factor of 40?

The greatest factor of 40 is 20.

• What is the sum of all factors of 40?

The sum of all factors of 40 is 90.

• What are multiples of 40?

First five multiples of 40 are 80, 120, 160, 200.

• What is the greatest prime factors of 40?

The greatest prime factor of 40 is 5.

• What are six multiples of 40?

First five multiples of 40 are 80, 120, 160, 200, 240, 280.

• What is prime factorization of 40?

Prime factorization of 40 is 2 x 2 x 2 x 5.

• Is 40 a whole number?

Yes 40 is a whole number.

#### Examples of Factors

Annie's mathematics teacher has asked her to find out all the positive and negative factors of 40? Help her in writing all the factors.

Positive factors are 1, 2, 4, 5, 8, 10, 20, 40.
Negative factors are -1, -2, -4, -5, -8, -10, -20, -40.

Can you help Sammy find out the product of the odd factors of 40?

Factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40.
Odd factors of 40 are 1, 5.
Hence product of odd factors of 40 is; 1 x 5 = 5.

Joey wants to write all the prime factors of 40 in exponential form, but he doesn't know how to do so can you assist him in this task?

Prime factors of 40 are 2, 2, 2, 5.
So in exponential form it can be written as 23 x 5.

How many factors are there for 40?

Factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40.
So there are in total 8 factors.

Kevin has been asked to write 7 factor(s) of 40. Can you predict the answer?

7 factor(s) of 40 are 1, 2, 4, 5, 8, 10, 20.

Sammy is puzzled while calculating the prime factors of 40. Can you help him find them?

Factors of 40 are 1, 2, 4, 5, 8, 10, 20, 40.
Prime factors of 40 are 2, 2, 2, 5

What is prime factorization of 40?

Prime factorization of 40 is 2 x 2 x 2 x 5 = 23 x 5.