Q: What is the prime factorization of the number 41,005,440?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5 x 7 x 113
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 5, 7, 113 }
  • Written in exponential form: 27 x 34 x 51 x 71 x 1131

Why is the prime factorization of 41,005,440 written as 27 x 34 x 51 x 71 x 1131?

What is prime factorization?

Prime factorization or prime factor decomposition is the process of finding which prime numbers can be multiplied together to make the original number.

Finding the prime factors of 41,005,440

To find the prime factors, you start by dividing the number by the first prime number, which is 2. If there is not a remainder, meaning you can divide evenly, then 2 is a factor of the number. Continue dividing by 2 until you cannot divide evenly anymore. Write down how many 2's you were able to divide by evenly. Now try dividing by the next prime factor, which is 3. The goal is to get to a quotient of 1.

If it doesn't make sense yet, let's try it...

Here are the first several prime factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...

Let's start by dividing 41,005,440 by 2

41,005,440 ÷ 2 = 20,502,720 - No remainder! 2 is one of the factors!
20,502,720 ÷ 2 = 10,251,360 - No remainder! 2 is one of the factors!
10,251,360 ÷ 2 = 5,125,680 - No remainder! 2 is one of the factors!
5,125,680 ÷ 2 = 2,562,840 - No remainder! 2 is one of the factors!
2,562,840 ÷ 2 = 1,281,420 - No remainder! 2 is one of the factors!
1,281,420 ÷ 2 = 640,710 - No remainder! 2 is one of the factors!
640,710 ÷ 2 = 320,355 - No remainder! 2 is one of the factors!
320,355 ÷ 2 = 160,177.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
320,355 ÷ 3 = 106,785 - No remainder! 3 is one of the factors!
106,785 ÷ 3 = 35,595 - No remainder! 3 is one of the factors!
35,595 ÷ 3 = 11,865 - No remainder! 3 is one of the factors!
11,865 ÷ 3 = 3,955 - No remainder! 3 is one of the factors!
3,955 ÷ 3 = 1,318.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
3,955 ÷ 5 = 791 - No remainder! 5 is one of the factors!
791 ÷ 5 = 158.2 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
791 ÷ 7 = 113 - No remainder! 7 is one of the factors!
113 ÷ 7 = 16.1429 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
113 ÷ 11 = 10.2727 - This has a remainder. 11 is not a factor.
113 ÷ 13 = 8.6923 - This has a remainder. 13 is not a factor.
113 ÷ 17 = 6.6471 - This has a remainder. 17 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
113 ÷ 113 = 1 - No remainder! 113 is one of the factors!

The orange divisor(s) above are the prime factors of the number 41,005,440. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 5 x 7 x 113 = 41,005,440. It can also be written in exponential form as 27 x 34 x 51 x 71 x 1131.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 41,005,440.

41,005,440
Factor Arrows
220,502,720
Factor Arrows
210,251,360
Factor Arrows
25,125,680
Factor Arrows
22,562,840
Factor Arrows
21,281,420
Factor Arrows
2640,710
Factor Arrows
2320,355
Factor Arrows
3106,785
Factor Arrows
335,595
Factor Arrows
311,865
Factor Arrows
33,955
Factor Arrows
5791
Factor Arrows
7113

More Prime Factorization Examples

41,005,43841,005,43941,005,44141,005,442
21 x 20,502,7191191 x 2,158,181141,005,441121 x 4,2831 x 4,7871

Try the factor calculator

Explore more about the number 41,005,440:


Ask a Question