Q: What is the prime factorization of the number 59,155,056?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 3 x 3 x 3 x 19 x 7,207
    • or also written as { 2, 2, 2, 2, 3, 3, 3, 19, 7,207 }
  • Written in exponential form: 24 x 33 x 191 x 7,2071

Why is the prime factorization of 59,155,056 written as 24 x 33 x 191 x 7,2071?

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 59,155,056

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 59,155,056 by 2

59,155,056 ÷ 2 = 29,577,528 - No remainder! 2 is one of the factors!
29,577,528 ÷ 2 = 14,788,764 - No remainder! 2 is one of the factors!
14,788,764 ÷ 2 = 7,394,382 - No remainder! 2 is one of the factors!
7,394,382 ÷ 2 = 3,697,191 - No remainder! 2 is one of the factors!
3,697,191 ÷ 2 = 1,848,595.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
3,697,191 ÷ 3 = 1,232,397 - No remainder! 3 is one of the factors!
1,232,397 ÷ 3 = 410,799 - No remainder! 3 is one of the factors!
410,799 ÷ 3 = 136,933 - No remainder! 3 is one of the factors!
136,933 ÷ 3 = 45,644.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
136,933 ÷ 5 = 27,386.6 - This has a remainder. 5 is not a factor.
136,933 ÷ 7 = 19,561.8571 - This has a remainder. 7 is not a factor.
136,933 ÷ 11 = 12,448.4545 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
136,933 ÷ 19 = 7,207 - No remainder! 19 is one of the factors!
7,207 ÷ 19 = 379.3158 - There is a remainder. We can't divide by 19 evenly anymore. Let's try the next prime number
7,207 ÷ 23 = 313.3478 - This has a remainder. 23 is not a factor.
7,207 ÷ 29 = 248.5172 - This has a remainder. 29 is not a factor.
7,207 ÷ 31 = 232.4839 - This has a remainder. 31 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
7,207 ÷ 7,207 = 1 - No remainder! 7,207 is one of the factors!

The orange divisor(s) above are the prime factors of the number 59,155,056. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 3 x 3 x 3 x 19 x 7,207 = 59,155,056. It can also be written in exponential form as 24 x 33 x 191 x 7,2071.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 59,155,056.

59,155,056
Factor Arrows
229,577,528
Factor Arrows
214,788,764
Factor Arrows
27,394,382
Factor Arrows
23,697,191
Factor Arrows
31,232,397
Factor Arrows
3410,799
Factor Arrows
3136,933
Factor Arrows
197,207

More Prime Factorization Examples

59,155,05459,155,05559,155,05759,155,058
21 x 72 x 603,623151 x 611 x 193,9511131 x 231 x 432 x 107121 x 29,577,5291

Try the factor calculator

Explore more about the number 59,155,056:


Ask a Question