Q: What is the prime factorization of the number 104,220,160?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 11 x 3,701
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 11, 3,701 }
  • Written in exponential form: 29 x 51 x 111 x 3,7011

Why is the prime factorization of 104,220,160 written as 29 x 51 x 111 x 3,7011?

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 104,220,160

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 104,220,160 by 2

104,220,160 ÷ 2 = 52,110,080 - No remainder! 2 is one of the factors!
52,110,080 ÷ 2 = 26,055,040 - No remainder! 2 is one of the factors!
26,055,040 ÷ 2 = 13,027,520 - No remainder! 2 is one of the factors!
13,027,520 ÷ 2 = 6,513,760 - No remainder! 2 is one of the factors!
6,513,760 ÷ 2 = 3,256,880 - No remainder! 2 is one of the factors!
3,256,880 ÷ 2 = 1,628,440 - No remainder! 2 is one of the factors!
1,628,440 ÷ 2 = 814,220 - No remainder! 2 is one of the factors!
814,220 ÷ 2 = 407,110 - No remainder! 2 is one of the factors!
407,110 ÷ 2 = 203,555 - No remainder! 2 is one of the factors!
203,555 ÷ 2 = 101,777.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
203,555 ÷ 3 = 67,851.6667 - This has a remainder. 3 is not a factor.
203,555 ÷ 5 = 40,711 - No remainder! 5 is one of the factors!
40,711 ÷ 5 = 8,142.2 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
40,711 ÷ 7 = 5,815.8571 - This has a remainder. 7 is not a factor.
40,711 ÷ 11 = 3,701 - No remainder! 11 is one of the factors!
3,701 ÷ 11 = 336.4545 - There is a remainder. We can't divide by 11 evenly anymore. Let's try the next prime number
3,701 ÷ 13 = 284.6923 - This has a remainder. 13 is not a factor.
3,701 ÷ 17 = 217.7059 - This has a remainder. 17 is not a factor.
3,701 ÷ 19 = 194.7895 - This has a remainder. 19 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
3,701 ÷ 3,701 = 1 - No remainder! 3,701 is one of the factors!

The orange divisor(s) above are the prime factors of the number 104,220,160. 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 5 x 11 x 3,701 = 104,220,160. It can also be written in exponential form as 29 x 51 x 111 x 3,7011.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 104,220,160.

104,220,160
Factor Arrows
252,110,080
Factor Arrows
226,055,040
Factor Arrows
213,027,520
Factor Arrows
26,513,760
Factor Arrows
23,256,880
Factor Arrows
21,628,440
Factor Arrows
2814,220
Factor Arrows
2407,110
Factor Arrows
2203,555
Factor Arrows
540,711
Factor Arrows
113,701

More Prime Factorization Examples

104,220,158104,220,159104,220,161104,220,162
21 x 72 x 1,063,471131 x 34,740,0531104,220,161121 x 33 x 1811 x 10,6631

Try the factor calculator

Explore more about the number 104,220,160:


Ask a Question