Q: What is the prime factorization of the number 40,253,440?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 3,931
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 3,931 }
  • Written in exponential form: 211 x 51 x 3,9311

Why is the prime factorization of 40,253,440 written as 211 x 51 x 3,9311?

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 40,253,440

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 40,253,440 by 2

40,253,440 ÷ 2 = 20,126,720 - No remainder! 2 is one of the factors!
20,126,720 ÷ 2 = 10,063,360 - No remainder! 2 is one of the factors!
10,063,360 ÷ 2 = 5,031,680 - No remainder! 2 is one of the factors!
5,031,680 ÷ 2 = 2,515,840 - No remainder! 2 is one of the factors!
2,515,840 ÷ 2 = 1,257,920 - No remainder! 2 is one of the factors!
1,257,920 ÷ 2 = 628,960 - No remainder! 2 is one of the factors!
628,960 ÷ 2 = 314,480 - No remainder! 2 is one of the factors!
314,480 ÷ 2 = 157,240 - No remainder! 2 is one of the factors!
157,240 ÷ 2 = 78,620 - No remainder! 2 is one of the factors!
78,620 ÷ 2 = 39,310 - No remainder! 2 is one of the factors!
39,310 ÷ 2 = 19,655 - No remainder! 2 is one of the factors!
19,655 ÷ 2 = 9,827.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
19,655 ÷ 3 = 6,551.6667 - This has a remainder. 3 is not a factor.
19,655 ÷ 5 = 3,931 - No remainder! 5 is one of the factors!
3,931 ÷ 5 = 786.2 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
3,931 ÷ 7 = 561.5714 - This has a remainder. 7 is not a factor.
3,931 ÷ 11 = 357.3636 - This has a remainder. 11 is not a factor.
3,931 ÷ 13 = 302.3846 - This has a remainder. 13 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
3,931 ÷ 3,931 = 1 - No remainder! 3,931 is one of the factors!

The orange divisor(s) above are the prime factors of the number 40,253,440. 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 2 x 2 x 2 x 2 x 5 x 3,931 = 40,253,440. It can also be written in exponential form as 211 x 51 x 3,9311.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 40,253,440.

40,253,440
Factor Arrows
220,126,720
Factor Arrows
210,063,360
Factor Arrows
25,031,680
Factor Arrows
22,515,840
Factor Arrows
21,257,920
Factor Arrows
2628,960
Factor Arrows
2314,480
Factor Arrows
2157,240
Factor Arrows
278,620
Factor Arrows
239,310
Factor Arrows
219,655
Factor Arrows
53,931

More Prime Factorization Examples

40,253,43840,253,43940,253,44140,253,442
21 x 191 x 311 x 34,171131 x 13,417,8131731 x 1911 x 2,887121 x 31 x 6,708,9071

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