Q: What is the prime factorization of the number 153,551,424?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 3 x 13 x 61,519
    • or also written as { 2, 2, 2, 2, 2, 2, 3, 13, 61,519 }
  • Written in exponential form: 26 x 31 x 131 x 61,5191

Why is the prime factorization of 153,551,424 written as 26 x 31 x 131 x 61,5191?

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 153,551,424

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 153,551,424 by 2

153,551,424 ÷ 2 = 76,775,712 - No remainder! 2 is one of the factors!
76,775,712 ÷ 2 = 38,387,856 - No remainder! 2 is one of the factors!
38,387,856 ÷ 2 = 19,193,928 - No remainder! 2 is one of the factors!
19,193,928 ÷ 2 = 9,596,964 - No remainder! 2 is one of the factors!
9,596,964 ÷ 2 = 4,798,482 - No remainder! 2 is one of the factors!
4,798,482 ÷ 2 = 2,399,241 - No remainder! 2 is one of the factors!
2,399,241 ÷ 2 = 1,199,620.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
2,399,241 ÷ 3 = 799,747 - No remainder! 3 is one of the factors!
799,747 ÷ 3 = 266,582.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
799,747 ÷ 5 = 159,949.4 - This has a remainder. 5 is not a factor.
799,747 ÷ 7 = 114,249.5714 - This has a remainder. 7 is not a factor.
799,747 ÷ 11 = 72,704.2727 - This has a remainder. 11 is not a factor.
799,747 ÷ 13 = 61,519 - No remainder! 13 is one of the factors!
61,519 ÷ 13 = 4,732.2308 - There is a remainder. We can't divide by 13 evenly anymore. Let's try the next prime number
61,519 ÷ 17 = 3,618.7647 - This has a remainder. 17 is not a factor.
61,519 ÷ 19 = 3,237.8421 - This has a remainder. 19 is not a factor.
61,519 ÷ 23 = 2,674.7391 - This has a remainder. 23 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
61,519 ÷ 61,519 = 1 - No remainder! 61,519 is one of the factors!

The orange divisor(s) above are the prime factors of the number 153,551,424. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 2 x 3 x 13 x 61,519 = 153,551,424. It can also be written in exponential form as 26 x 31 x 131 x 61,5191.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 153,551,424.

153,551,424
Factor Arrows
276,775,712
Factor Arrows
238,387,856
Factor Arrows
219,193,928
Factor Arrows
29,596,964
Factor Arrows
24,798,482
Factor Arrows
22,399,241
Factor Arrows
3799,747
Factor Arrows
1361,519

More Prime Factorization Examples

153,551,422153,551,423153,551,425153,551,426
21 x 4,3631 x 17,5971153,551,423152 x 6,142,057121 x 71 x 191 x 2271 x 2,5431

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