Q: What is the prime factorization of the number 109,444,352?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 427,517
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 427,517 }
  • Written in exponential form: 28 x 427,5171

Why is the prime factorization of 109,444,352 written as 28 x 427,5171?

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 109,444,352

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 109,444,352 by 2

109,444,352 ÷ 2 = 54,722,176 - No remainder! 2 is one of the factors!
54,722,176 ÷ 2 = 27,361,088 - No remainder! 2 is one of the factors!
27,361,088 ÷ 2 = 13,680,544 - No remainder! 2 is one of the factors!
13,680,544 ÷ 2 = 6,840,272 - No remainder! 2 is one of the factors!
6,840,272 ÷ 2 = 3,420,136 - No remainder! 2 is one of the factors!
3,420,136 ÷ 2 = 1,710,068 - No remainder! 2 is one of the factors!
1,710,068 ÷ 2 = 855,034 - No remainder! 2 is one of the factors!
855,034 ÷ 2 = 427,517 - No remainder! 2 is one of the factors!
427,517 ÷ 2 = 213,758.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
427,517 ÷ 3 = 142,505.6667 - This has a remainder. 3 is not a factor.
427,517 ÷ 5 = 85,503.4 - This has a remainder. 5 is not a factor.
427,517 ÷ 7 = 61,073.8571 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
427,517 ÷ 427,517 = 1 - No remainder! 427,517 is one of the factors!

The orange divisor(s) above are the prime factors of the number 109,444,352. 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 427,517 = 109,444,352. It can also be written in exponential form as 28 x 427,5171.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 109,444,352.

109,444,352
Factor Arrows
254,722,176
Factor Arrows
227,361,088
Factor Arrows
213,680,544
Factor Arrows
26,840,272
Factor Arrows
23,420,136
Factor Arrows
21,710,068
Factor Arrows
2855,034
Factor Arrows
2427,517

More Prime Factorization Examples

109,444,350109,444,351109,444,353109,444,354
21 x 31 x 52 x 231 x 31,7231171 x 191 x 591 x 5,743131 x 311 x 8271 x 1,423121 x 1,0631 x 51,4791

Try the factor calculator

Explore more about the number 109,444,352:


Ask a Question