Q: What is the prime factorization of the number 2,110,752?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 7 x 349
    • or also written as { 2, 2, 2, 2, 2, 3, 3, 3, 7, 349 }
  • Written in exponential form: 25 x 33 x 71 x 3491

Why is the prime factorization of 2,110,752 written as 25 x 33 x 71 x 3491?

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 2,110,752

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 2,110,752 by 2

2,110,752 ÷ 2 = 1,055,376 - No remainder! 2 is one of the factors!
1,055,376 ÷ 2 = 527,688 - No remainder! 2 is one of the factors!
527,688 ÷ 2 = 263,844 - No remainder! 2 is one of the factors!
263,844 ÷ 2 = 131,922 - No remainder! 2 is one of the factors!
131,922 ÷ 2 = 65,961 - No remainder! 2 is one of the factors!
65,961 ÷ 2 = 32,980.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
65,961 ÷ 3 = 21,987 - No remainder! 3 is one of the factors!
21,987 ÷ 3 = 7,329 - No remainder! 3 is one of the factors!
7,329 ÷ 3 = 2,443 - No remainder! 3 is one of the factors!
2,443 ÷ 3 = 814.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
2,443 ÷ 5 = 488.6 - This has a remainder. 5 is not a factor.
2,443 ÷ 7 = 349 - No remainder! 7 is one of the factors!
349 ÷ 7 = 49.8571 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
349 ÷ 11 = 31.7273 - This has a remainder. 11 is not a factor.
349 ÷ 13 = 26.8462 - This has a remainder. 13 is not a factor.
349 ÷ 17 = 20.5294 - This has a remainder. 17 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
349 ÷ 349 = 1 - No remainder! 349 is one of the factors!

The orange divisor(s) above are the prime factors of the number 2,110,752. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 7 x 349 = 2,110,752. It can also be written in exponential form as 25 x 33 x 71 x 3491.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 2,110,752.

2,110,752
Factor Arrows
21,055,376
Factor Arrows
2527,688
Factor Arrows
2263,844
Factor Arrows
2131,922
Factor Arrows
265,961
Factor Arrows
321,987
Factor Arrows
37,329
Factor Arrows
32,443
Factor Arrows
7349

More Prime Factorization Examples

2,110,7502,110,7512,110,7532,110,754
21 x 53 x 8,44312,110,75112,110,753121 x 171 x 62,0811

Try the factor calculator

Explore more about the number 2,110,752:


Ask a Question