Q: What is the prime factorization of the number 3,633,541?

 A:
  • The prime factors are: 19 x 31 x 31 x 199
    • or also written as { 19, 31, 31, 199 }
  • Written in exponential form: 191 x 312 x 1991

Why is the prime factorization of 3,633,541 written as 191 x 312 x 1991?

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 3,633,541

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 3,633,541 by 2

3,633,541 ÷ 2 = 1,816,770.5 - This has a remainder. Let's try another prime number.
3,633,541 ÷ 3 = 1,211,180.3333 - This has a remainder. Let's try another prime number.
3,633,541 ÷ 5 = 726,708.2 - This has a remainder. Let's try another prime number.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
3,633,541 ÷ 19 = 191,239 - No remainder! 19 is one of the factors!
191,239 ÷ 19 = 10,065.2105 - There is a remainder. We can't divide by 19 evenly anymore. Let's try the next prime number
191,239 ÷ 23 = 8,314.7391 - This has a remainder. 23 is not a factor.
191,239 ÷ 29 = 6,594.4483 - This has a remainder. 29 is not a factor.
191,239 ÷ 31 = 6,169 - No remainder! 31 is one of the factors!
6,169 ÷ 31 = 199 - No remainder! 31 is one of the factors!
199 ÷ 31 = 6.4194 - There is a remainder. We can't divide by 31 evenly anymore. Let's try the next prime number
199 ÷ 37 = 5.3784 - This has a remainder. 37 is not a factor.
199 ÷ 41 = 4.8537 - This has a remainder. 41 is not a factor.
199 ÷ 43 = 4.6279 - This has a remainder. 43 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
199 ÷ 199 = 1 - No remainder! 199 is one of the factors!

The orange divisor(s) above are the prime factors of the number 3,633,541. If we put all of it together we have the factors 19 x 31 x 31 x 199 = 3,633,541. It can also be written in exponential form as 191 x 312 x 1991.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 3,633,541.

3,633,541
Factor Arrows
19191,239
Factor Arrows
316,169
Factor Arrows
31199

More Prime Factorization Examples

3,633,5393,633,5403,633,5423,633,543
71 x 131 x 39,929122 x 31 x 51 x 231 x 2,633121 x 111 x 165,161132 x 411 x 431 x 2291

Try the factor calculator

Explore more about the number 3,633,541:


Ask a Question