Q: What is the prime factorization of the number 3,492,480?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 5 x 17 x 107
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 3, 5, 17, 107 }
  • Written in exponential form: 27 x 31 x 51 x 171 x 1071

Why is the prime factorization of 3,492,480 written as 27 x 31 x 51 x 171 x 1071?

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 3,492,480

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 3,492,480 by 2

3,492,480 ÷ 2 = 1,746,240 - No remainder! 2 is one of the factors!
1,746,240 ÷ 2 = 873,120 - No remainder! 2 is one of the factors!
873,120 ÷ 2 = 436,560 - No remainder! 2 is one of the factors!
436,560 ÷ 2 = 218,280 - No remainder! 2 is one of the factors!
218,280 ÷ 2 = 109,140 - No remainder! 2 is one of the factors!
109,140 ÷ 2 = 54,570 - No remainder! 2 is one of the factors!
54,570 ÷ 2 = 27,285 - No remainder! 2 is one of the factors!
27,285 ÷ 2 = 13,642.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
27,285 ÷ 3 = 9,095 - No remainder! 3 is one of the factors!
9,095 ÷ 3 = 3,031.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
9,095 ÷ 5 = 1,819 - No remainder! 5 is one of the factors!
1,819 ÷ 5 = 363.8 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
1,819 ÷ 7 = 259.8571 - This has a remainder. 7 is not a factor.
1,819 ÷ 11 = 165.3636 - This has a remainder. 11 is not a factor.
1,819 ÷ 13 = 139.9231 - This has a remainder. 13 is not a factor.
1,819 ÷ 17 = 107 - No remainder! 17 is one of the factors!
107 ÷ 17 = 6.2941 - There is a remainder. We can't divide by 17 evenly anymore. Let's try the next prime number
107 ÷ 19 = 5.6316 - This has a remainder. 19 is not a factor.
107 ÷ 23 = 4.6522 - This has a remainder. 23 is not a factor.
107 ÷ 29 = 3.6897 - This has a remainder. 29 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
107 ÷ 107 = 1 - No remainder! 107 is one of the factors!

The orange divisor(s) above are the prime factors of the number 3,492,480. 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 3 x 5 x 17 x 107 = 3,492,480. It can also be written in exponential form as 27 x 31 x 51 x 171 x 1071.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 3,492,480.

3,492,480
Factor Arrows
21,746,240
Factor Arrows
2873,120
Factor Arrows
2436,560
Factor Arrows
2218,280
Factor Arrows
2109,140
Factor Arrows
254,570
Factor Arrows
227,285
Factor Arrows
39,095
Factor Arrows
51,819
Factor Arrows
17107

More Prime Factorization Examples

3,492,4783,492,4793,492,4813,492,482
21 x 111 x 158,74911011 x 1511 x 2291231 x 151,847121 x 71 x 249,4631

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