Q: What is the prime factorization of the number 1,462,272?

 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 7 x 17
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 7, 17 }
  • Written in exponential form: 212 x 31 x 71 x 171

Why is the prime factorization of 1,462,272 written as 212 x 31 x 71 x 171?

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 1,462,272

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 1,462,272 by 2

1,462,272 ÷ 2 = 731,136 - No remainder! 2 is one of the factors!
731,136 ÷ 2 = 365,568 - No remainder! 2 is one of the factors!
365,568 ÷ 2 = 182,784 - No remainder! 2 is one of the factors!
182,784 ÷ 2 = 91,392 - No remainder! 2 is one of the factors!
91,392 ÷ 2 = 45,696 - No remainder! 2 is one of the factors!
45,696 ÷ 2 = 22,848 - No remainder! 2 is one of the factors!
22,848 ÷ 2 = 11,424 - No remainder! 2 is one of the factors!
11,424 ÷ 2 = 5,712 - No remainder! 2 is one of the factors!
5,712 ÷ 2 = 2,856 - No remainder! 2 is one of the factors!
2,856 ÷ 2 = 1,428 - No remainder! 2 is one of the factors!
1,428 ÷ 2 = 714 - No remainder! 2 is one of the factors!
714 ÷ 2 = 357 - No remainder! 2 is one of the factors!
357 ÷ 2 = 178.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
357 ÷ 3 = 119 - No remainder! 3 is one of the factors!
119 ÷ 3 = 39.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
119 ÷ 5 = 23.8 - This has a remainder. 5 is not a factor.
119 ÷ 7 = 17 - No remainder! 7 is one of the factors!
17 ÷ 7 = 2.4286 - There is a remainder. We can't divide by 7 evenly anymore. Let's try the next prime number
17 ÷ 11 = 1.5455 - This has a remainder. 11 is not a factor.
17 ÷ 13 = 1.3077 - This has a remainder. 13 is not a factor.
17 ÷ 17 = 1 - No remainder! 17 is one of the factors!

The orange divisor(s) above are the prime factors of the number 1,462,272. 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 7 x 17 = 1,462,272. It can also be written in exponential form as 212 x 31 x 71 x 171.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 1,462,272.

1,462,272
Factor Arrows
2731,136
Factor Arrows
2365,568
Factor Arrows
2182,784
Factor Arrows
291,392
Factor Arrows
245,696
Factor Arrows
222,848
Factor Arrows
211,424
Factor Arrows
25,712
Factor Arrows
22,856
Factor Arrows
21,428
Factor Arrows
2714
Factor Arrows
2357
Factor Arrows
3119
Factor Arrows
717

More Prime Factorization Examples

1,462,2701,462,2711,462,2731,462,274
21 x 51 x 311 x 531 x 891231 x 63,57711631 x 8,971121 x 111 x 66,4671

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