How To Find The Prime Factors Of 40 By Prime Factorization Method?

Factors of 40 are the numbers that can divide the original number 40 and results in the whole number as quotient. Basically, when we multiply any two factors in pairs we get the original number. Whereas multiples of 40 are the extended times of it, such as 40, 80, 120, 160, 200, 240 and so on. This is the difference between factors and multiples. 40 is a composite number same as 36, 24, 18, 60, 45, etc and have more than 2 factors. We will find out here factors in pairs and prime factors of number 40. Here, we are going to learn the factors of 40, and the pair factors and the prime factors of 40 by the prime factorization method.

Table of Contents:

• What are the Factors of 40?
• Pair Factors of 40
• Factors of 40 by Division Method
• Prime Factorization of 40
• Solved Examples
• FAQs

What are the Factors of 40?

The numbers that divide 40 exactly without leaving a remainder are the factors of 40. In other words, the factors of 40 are the numbers that are multiplied in pairs resulting in an original number. As the number 40 is an even composite number, it has many factors other than 1 and 40. Therefore, 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

Pair Factors of 40

The pair factors of 40 are the numbers that are multiplied together and result in an original number 40. The pair factors of 40 can be in positive or negative pairs. If we multiply the pair of negative numbers, it will give the original number 40. The positive and negative pair factors of 40 are given below:

Positive Pair Factors of 40:

Positive Factors of 40	Positive Pair Factors of 40
1 × 40	(1, 40)
2 × 20	(2, 20)
4 × 10	(4, 10)
5 × 8	(5, 8)

Negative Pair Factors of 40:

Negative Factors of 40	Negative Pair Factors of 40
-1 × -40	(-1, -40)
-2 × -20	(-2, -20)
-4 × -10	(-4, -10)
-5 × -8	(-5, -8)

Factors of 40 by Division Method

The factors of 40 can be found using the division method. In division method, we need to divide 40 by different consecutive integers. The integers that divide 40 exactly without leaving any remainder are the factors of 40. Now, let’s start dividing 40 by 1.

• 40/1 = 40 (Factor 1 and remainder 0)
• 40/2 = 20 (Factor 2 and remainder 0)
• 40/4 = 10 ( Factor 4 and remainder 0)
• 40/5 = 8 (Factor 5 and remainder 0)
• 40/8 = 5 (Factor 8 and remainder 0)
• 40/10 = 4 (Factor 10 and remainder 0)
• 40/20 = 2 (Factor 20 and remainder 0)
• 40/40 = 1 (Factor 40 and remainder 0)

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

Note:

If we divide 40 by any numbers other than 1, 2, 4, 5, 8, 10, 20 and 40, it leaves the remainder and hence, they are not the factors of 40.

Prime Factorization of 40

The number 40 is a composite number, now let us find its prime factors.

• The first step is to divide the number 40 with the smallest prime factor,i.e. 2.

40 ÷ 2 = 20

           Again, divide 20 by 2.

20 ÷ 2 = 10

• Keep on dividing unless you get an odd number, as we know any odd number if divided by 2 gives a fraction. And we cannot consider a fraction as a factor. Therefore,

 10 ÷ 2 = 5

          Now, if we divide 5 by 2 we get a fraction number.

• Now, proceed to the next prime numbers, i.e. 3, 5, 7 and so on.

5 ÷ 3 = 1.67; not a factor.

          Move to the next prime number, 5.

• Dividing 5 by 5 we get,

5 ÷ 5 = 1

• We have received 1 at the end and further, we cannot proceed with the division method. So, the prime factorisation of 40 are 2 × 2 × 2 × 5 or 23 × 5, where 2 and 5 are the prime numbers.

Video Lesson on Prime Factors

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Examples

Example 1:

Find the common factors of 40 and 41.

Solution:

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

The factors of 41 are 1 and 41.

As the number 41 is a prime number, the common factor of 40 and 41 is 1.

Example 2:

Find the common factors of 40 and 39.

Solution:

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

Factors of 39 = 1, 3, 13 and 39.

Hence, the common factor of 40 and 39 is 1.

Example 3:

Find the common factors of 40 and 80.

Solution:

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

The factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80.

Therefore, the common factors of 40 and 80 are 1, 2, 4, 5, 8, 10, 20 and 40.

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Frequently Asked Questions on Factors of 40

Q1

What are the factors of 40?

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

Q2

What is the prime factorization of 40?

The prime factorization of 40 is 2 × 2 × 2 × 5 or 23 × 5.

Q3

What are the positive pair factors of 40?

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

Q4

What are the negative pair factors of 40?

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

Q5

Is 16 a factor of 40?

No, 16 is not a factor of 40. If 40 is divided by 16, it leaves a remainder, and hence 16 is not a factor of 40.

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