Q: What is the prime factorization of the number 162,553,504?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 503 x 10,099
    • or also written as { 2, 2, 2, 2, 2, 503, 10,099 }
  • Written in exponential form: 25 x 5031 x 10,0991

Why is the prime factorization of 162,553,504 written as 25 x 5031 x 10,0991?

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 162,553,504

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 162,553,504 by 2

162,553,504 ÷ 2 = 81,276,752 - No remainder! 2 is one of the factors!
81,276,752 ÷ 2 = 40,638,376 - No remainder! 2 is one of the factors!
40,638,376 ÷ 2 = 20,319,188 - No remainder! 2 is one of the factors!
20,319,188 ÷ 2 = 10,159,594 - No remainder! 2 is one of the factors!
10,159,594 ÷ 2 = 5,079,797 - No remainder! 2 is one of the factors!
5,079,797 ÷ 2 = 2,539,898.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
5,079,797 ÷ 3 = 1,693,265.6667 - This has a remainder. 3 is not a factor.
5,079,797 ÷ 5 = 1,015,959.4 - This has a remainder. 5 is not a factor.
5,079,797 ÷ 7 = 725,685.2857 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
5,079,797 ÷ 503 = 10,099 - No remainder! 503 is one of the factors!
10,099 ÷ 503 = 20.0775 - There is a remainder. We can't divide by 503 evenly anymore. Let's try the next prime number
10,099 ÷ 509 = 19.8409 - This has a remainder. 509 is not a factor.
10,099 ÷ 521 = 19.3839 - This has a remainder. 521 is not a factor.
10,099 ÷ 523 = 19.3098 - This has a remainder. 523 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
10,099 ÷ 10,099 = 1 - No remainder! 10,099 is one of the factors!

The orange divisor(s) above are the prime factors of the number 162,553,504. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 503 x 10,099 = 162,553,504. It can also be written in exponential form as 25 x 5031 x 10,0991.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 162,553,504.

162,553,504
Factor Arrows
281,276,752
Factor Arrows
240,638,376
Factor Arrows
220,319,188
Factor Arrows
210,159,594
Factor Arrows
25,079,797
Factor Arrows
50310,099

More Prime Factorization Examples

162,553,502162,553,503162,553,505162,553,506
21 x 431 x 2831 x 6,679131 x 71 x 7,740,643151 x 32,510,701121 x 31 x 371 x 711 x 10,3131

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