Q: What is the prime factorization of the number 35,500,544?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 69,337
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 69,337 }
  • Written in exponential form: 29 x 69,3371

Why is the prime factorization of 35,500,544 written as 29 x 69,3371?

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 35,500,544

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 35,500,544 by 2

35,500,544 ÷ 2 = 17,750,272 - No remainder! 2 is one of the factors!
17,750,272 ÷ 2 = 8,875,136 - No remainder! 2 is one of the factors!
8,875,136 ÷ 2 = 4,437,568 - No remainder! 2 is one of the factors!
4,437,568 ÷ 2 = 2,218,784 - No remainder! 2 is one of the factors!
2,218,784 ÷ 2 = 1,109,392 - No remainder! 2 is one of the factors!
1,109,392 ÷ 2 = 554,696 - No remainder! 2 is one of the factors!
554,696 ÷ 2 = 277,348 - No remainder! 2 is one of the factors!
277,348 ÷ 2 = 138,674 - No remainder! 2 is one of the factors!
138,674 ÷ 2 = 69,337 - No remainder! 2 is one of the factors!
69,337 ÷ 2 = 34,668.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
69,337 ÷ 3 = 23,112.3333 - This has a remainder. 3 is not a factor.
69,337 ÷ 5 = 13,867.4 - This has a remainder. 5 is not a factor.
69,337 ÷ 7 = 9,905.2857 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
69,337 ÷ 69,337 = 1 - No remainder! 69,337 is one of the factors!

The orange divisor(s) above are the prime factors of the number 35,500,544. 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 69,337 = 35,500,544. It can also be written in exponential form as 29 x 69,3371.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 35,500,544.

35,500,544
Factor Arrows
217,750,272
Factor Arrows
28,875,136
Factor Arrows
24,437,568
Factor Arrows
22,218,784
Factor Arrows
21,109,392
Factor Arrows
2554,696
Factor Arrows
2277,348
Factor Arrows
2138,674
Factor Arrows
269,337

More Prime Factorization Examples

35,500,54235,500,54335,500,54535,500,546
21 x 31 x 71 x 111 x 431 x 1,7871131 x 2,730,811133 x 51 x 971 x 2,711121 x 231 x 791 x 9,7691

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