Q: What is the prime factorization of the number 17,745,152?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 69,317
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 69,317 }
  • Written in exponential form: 28 x 69,3171

Why is the prime factorization of 17,745,152 written as 28 x 69,3171?

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 17,745,152

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 17,745,152 by 2

17,745,152 ÷ 2 = 8,872,576 - No remainder! 2 is one of the factors!
8,872,576 ÷ 2 = 4,436,288 - No remainder! 2 is one of the factors!
4,436,288 ÷ 2 = 2,218,144 - No remainder! 2 is one of the factors!
2,218,144 ÷ 2 = 1,109,072 - No remainder! 2 is one of the factors!
1,109,072 ÷ 2 = 554,536 - No remainder! 2 is one of the factors!
554,536 ÷ 2 = 277,268 - No remainder! 2 is one of the factors!
277,268 ÷ 2 = 138,634 - No remainder! 2 is one of the factors!
138,634 ÷ 2 = 69,317 - No remainder! 2 is one of the factors!
69,317 ÷ 2 = 34,658.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
69,317 ÷ 3 = 23,105.6667 - This has a remainder. 3 is not a factor.
69,317 ÷ 5 = 13,863.4 - This has a remainder. 5 is not a factor.
69,317 ÷ 7 = 9,902.4286 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
69,317 ÷ 69,317 = 1 - No remainder! 69,317 is one of the factors!

The orange divisor(s) above are the prime factors of the number 17,745,152. 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 69,317 = 17,745,152. It can also be written in exponential form as 28 x 69,3171.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 17,745,152.

17,745,152
Factor Arrows
28,872,576
Factor Arrows
24,436,288
Factor Arrows
22,218,144
Factor Arrows
21,109,072
Factor Arrows
2554,536
Factor Arrows
2277,268
Factor Arrows
2138,634
Factor Arrows
269,317

More Prime Factorization Examples

17,745,15017,745,15117,745,15317,745,154
21 x 31 x 52 x 2811 x 4211671 x 831 x 3,191131 x 5,915,051121 x 72 x 431 x 4,2111

Try the factor calculator

Explore more about the number 17,745,152:


Ask a Question