Q: What is the prime factorization of the number 3,353,856?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 11 x 397
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 3, 11, 397 }
  • Written in exponential form: 28 x 31 x 111 x 3971

Why is the prime factorization of 3,353,856 written as 28 x 31 x 111 x 3971?

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 3,353,856

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 3,353,856 by 2

3,353,856 ÷ 2 = 1,676,928 - No remainder! 2 is one of the factors!
1,676,928 ÷ 2 = 838,464 - No remainder! 2 is one of the factors!
838,464 ÷ 2 = 419,232 - No remainder! 2 is one of the factors!
419,232 ÷ 2 = 209,616 - No remainder! 2 is one of the factors!
209,616 ÷ 2 = 104,808 - No remainder! 2 is one of the factors!
104,808 ÷ 2 = 52,404 - No remainder! 2 is one of the factors!
52,404 ÷ 2 = 26,202 - No remainder! 2 is one of the factors!
26,202 ÷ 2 = 13,101 - No remainder! 2 is one of the factors!
13,101 ÷ 2 = 6,550.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
13,101 ÷ 3 = 4,367 - No remainder! 3 is one of the factors!
4,367 ÷ 3 = 1,455.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
4,367 ÷ 5 = 873.4 - This has a remainder. 5 is not a factor.
4,367 ÷ 7 = 623.8571 - This has a remainder. 7 is not a factor.
4,367 ÷ 11 = 397 - No remainder! 11 is one of the factors!
397 ÷ 11 = 36.0909 - There is a remainder. We can't divide by 11 evenly anymore. Let's try the next prime number
397 ÷ 13 = 30.5385 - This has a remainder. 13 is not a factor.
397 ÷ 17 = 23.3529 - This has a remainder. 17 is not a factor.
397 ÷ 19 = 20.8947 - This has a remainder. 19 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
397 ÷ 397 = 1 - No remainder! 397 is one of the factors!

The orange divisor(s) above are the prime factors of the number 3,353,856. 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 3 x 11 x 397 = 3,353,856. It can also be written in exponential form as 28 x 31 x 111 x 3971.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 3,353,856.

3,353,856
Factor Arrows
21,676,928
Factor Arrows
2838,464
Factor Arrows
2419,232
Factor Arrows
2209,616
Factor Arrows
2104,808
Factor Arrows
252,404
Factor Arrows
226,202
Factor Arrows
213,101
Factor Arrows
34,367
Factor Arrows
11397

More Prime Factorization Examples

3,353,8543,353,8553,353,8573,353,858
21 x 73 x 4,889151 x 591 x 11,3691131 x 257,989121 x 6771 x 2,4771

Try the factor calculator

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