Factors Of 40 | With Easy Division and Prime Factorization

In maths, factors of 40 are the numbers that divide the original number 40 and produce the whole number in quotient form. You can find the original number by multiplying any two factors in pairs. Likewise, multiples of 40 are the lengthened versions, such as 40, 80, 120, 160, 200, 240, and so on. 

Factors and multiples have different properties. A composite number is a number that has more than two factors, such as 36, 24, 18, 60, 45, etc. Here I will discuss factors in pairs and prime factors of number 40. 

I will analyze 40, its pair factors, and its prime factors by the prime factorization method.

What are the Factors of 40?

A factor of 40 is a number that divides 40 without leaving a remainder. To explain this further, the factors of 40 are the numbers multiplied in pairs, resulting in a new number. 

It has many factors other than 1 and 40 because it is an even composite number. 

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

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

Prime Factorization of 40: 2×2×2×5 or 2³ × 5

What are the Factors of -40?

Factors of -40: -1, -2, -4, -5, -8, -10, -20 and -40.

We can get -40 by having (-1, 40), (-2, 20), (-4, 10), and  (-5, 8)as a pair of factors. Similarly, we can also get -40 by having (1, -40), (2, -20), (4, -10), and (5, -8) as a pair of factors.

Pair Factors of 40

A pair factor of 40 is the result of multiplying two numbers together that result in an original number of 40. They can either be positive or negative pairs. 

This will give us the original number 40 when we multiply the two negative numbers. Here are the positive and negative factors of 40:

Positive Pair Factors of 40:

Negative Pair Factors of 40:

Factors of 40 by Division Method

You can also find the factors of 40 by using the division method. To divide 40 using the division method, we must divide it by successive integers. Factors of 40 are the integers that divide 40 exactly without leaving any remainder. 

Let’s now divide 40 by 1.

• 40/1 = 40     
• 40/2 = 20    
• 40/4 = 10      
• 40/5 = 8         
• 40/8 = 5 
• 40/10 = 4
• 40/20 = 2 
• 40/40 = 1 

As a result, the factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.

Note:

When we divide 40 by any number other than 1, 2, 4, 5, 8, 10, 20, and 40, it leaves the remainder, and therefore, it is not a factor of 40.

Prime Factorization of 40

Now that we know 40 is a composite number let’s find its prime factors.

First, we need to divide 40 by the smallest prime factor, i.e., 2.

40 ÷ 2 = 20

           Divide 20 by 2, once more.

20 ÷ 2 = 10

Divide until you get an odd number because you get a fraction if you divide by 2. Fractions cannot be factors. Therefore,

 10 ÷ 2 = 5

Dividing 5 by 2 gives us a fraction.

Next, consider prime numbers 3, 5, 7, and so on.

5 ÷ 3 = 1.67; not a factor

Next, we will move to the number 5.

If we divide 5 by 5, we get:

5 ÷ 5 = 1

Moreover, we received one at the end, so we cannot use the division method.

As a result, the prime factorization of 40 is 2 x 2 x 2 x 5 or 2³ x 5, where 2 and 5 are prime numbers.

Examples

Example 1:

Find the factors that are common to 35 and 41.

Solution:

The factors of 35 are 1, 5, 7, and 35.

1 and 41 are the factors of 41.

Since 41 is a prime number, the common factor between 35 and 41 is 1.

Example 2:

Find the common factor between 40 and 24.

Solution:

The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40.

Factors of 24 = 1, 2, 3, 4, 6, 8, 12, and 24.

Therefore, 40 and 39 have a common factor of 1,2,4 and 8.

Example 3:

Calculate the common factors of 40 and 64.

Solution:

40 has the following factors: 1, 2, 4, 5, 8, 10, 20, and 40.

Factors of 64 = 1, 2, 4, 8, 16, 32, and 64.

As a result, 40 and 64 share these common factors: 1, 2, 4, 8, and 10.

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