Q: What is the prime factorization of the number 3,477,504?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 283
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 283 }
  • Written in exponential form: 212 x 31 x 2831

Why is the prime factorization of 3,477,504 written as 212 x 31 x 2831?

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 3,477,504

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 3,477,504 by 2

3,477,504 ÷ 2 = 1,738,752 - No remainder! 2 is one of the factors!
1,738,752 ÷ 2 = 869,376 - No remainder! 2 is one of the factors!
869,376 ÷ 2 = 434,688 - No remainder! 2 is one of the factors!
434,688 ÷ 2 = 217,344 - No remainder! 2 is one of the factors!
217,344 ÷ 2 = 108,672 - No remainder! 2 is one of the factors!
108,672 ÷ 2 = 54,336 - No remainder! 2 is one of the factors!
54,336 ÷ 2 = 27,168 - No remainder! 2 is one of the factors!
27,168 ÷ 2 = 13,584 - No remainder! 2 is one of the factors!
13,584 ÷ 2 = 6,792 - No remainder! 2 is one of the factors!
6,792 ÷ 2 = 3,396 - No remainder! 2 is one of the factors!
3,396 ÷ 2 = 1,698 - No remainder! 2 is one of the factors!
1,698 ÷ 2 = 849 - No remainder! 2 is one of the factors!
849 ÷ 2 = 424.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
849 ÷ 3 = 283 - No remainder! 3 is one of the factors!
283 ÷ 3 = 94.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
283 ÷ 5 = 56.6 - This has a remainder. 5 is not a factor.
283 ÷ 7 = 40.4286 - This has a remainder. 7 is not a factor.
283 ÷ 11 = 25.7273 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
283 ÷ 283 = 1 - No remainder! 283 is one of the factors!

The orange divisor(s) above are the prime factors of the number 3,477,504. 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 2 x 2 x 2 x 2 x 3 x 283 = 3,477,504. It can also be written in exponential form as 212 x 31 x 2831.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 3,477,504.

3,477,504
Factor Arrows
21,738,752
Factor Arrows
2869,376
Factor Arrows
2434,688
Factor Arrows
2217,344
Factor Arrows
2108,672
Factor Arrows
254,336
Factor Arrows
227,168
Factor Arrows
213,584
Factor Arrows
26,792
Factor Arrows
23,396
Factor Arrows
21,698
Factor Arrows
2849
Factor Arrows
3283

More Prime Factorization Examples

3,477,5023,477,5033,477,5053,477,506
21 x 71 x 1391 x 1,7871171 x 3371 x 607151 x 4491 x 1,549121 x 291 x 59,9571

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