Q: What is the prime factorization of the number 121,464,032?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 67 x 181 x 313
    • or also written as { 2, 2, 2, 2, 2, 67, 181, 313 }
  • Written in exponential form: 25 x 671 x 1811 x 3131

Why is the prime factorization of 121,464,032 written as 25 x 671 x 1811 x 3131?

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 121,464,032

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 121,464,032 by 2

121,464,032 ÷ 2 = 60,732,016 - No remainder! 2 is one of the factors!
60,732,016 ÷ 2 = 30,366,008 - No remainder! 2 is one of the factors!
30,366,008 ÷ 2 = 15,183,004 - No remainder! 2 is one of the factors!
15,183,004 ÷ 2 = 7,591,502 - No remainder! 2 is one of the factors!
7,591,502 ÷ 2 = 3,795,751 - No remainder! 2 is one of the factors!
3,795,751 ÷ 2 = 1,897,875.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
3,795,751 ÷ 3 = 1,265,250.3333 - This has a remainder. 3 is not a factor.
3,795,751 ÷ 5 = 759,150.2 - This has a remainder. 5 is not a factor.
3,795,751 ÷ 7 = 542,250.1429 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
3,795,751 ÷ 67 = 56,653 - No remainder! 67 is one of the factors!
56,653 ÷ 67 = 845.5672 - There is a remainder. We can't divide by 67 evenly anymore. Let's try the next prime number
56,653 ÷ 71 = 797.9296 - This has a remainder. 71 is not a factor.
56,653 ÷ 73 = 776.0685 - This has a remainder. 73 is not a factor.
56,653 ÷ 79 = 717.1266 - This has a remainder. 79 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
56,653 ÷ 181 = 313 - No remainder! 181 is one of the factors!
313 ÷ 181 = 1.7293 - There is a remainder. We can't divide by 181 evenly anymore. Let's try the next prime number
313 ÷ 191 = 1.6387 - This has a remainder. 191 is not a factor.
313 ÷ 193 = 1.6218 - This has a remainder. 193 is not a factor.
313 ÷ 197 = 1.5888 - This has a remainder. 197 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
313 ÷ 313 = 1 - No remainder! 313 is one of the factors!

The orange divisor(s) above are the prime factors of the number 121,464,032. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 67 x 181 x 313 = 121,464,032. It can also be written in exponential form as 25 x 671 x 1811 x 3131.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 121,464,032.

121,464,032
Factor Arrows
260,732,016
Factor Arrows
230,366,008
Factor Arrows
215,183,004
Factor Arrows
27,591,502
Factor Arrows
23,795,751
Factor Arrows
6756,653
Factor Arrows
181313

More Prime Factorization Examples

121,464,030121,464,031121,464,033121,464,034
21 x 31 x 51 x 1791 x 22,6191131 x 171 x 711 x 7,741131 x 40,488,011121 x 3,0831 x 19,6991

Try the factor calculator

Explore more about the number 121,464,032:


Ask a Question