Q: What is the prime factorization of the number 15,162,480?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 3 x 3 x 5 x 21,059
    • or also written as { 2, 2, 2, 2, 3, 3, 5, 21,059 }
  • Written in exponential form: 24 x 32 x 51 x 21,0591

Why is the prime factorization of 15,162,480 written as 24 x 32 x 51 x 21,0591?

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 15,162,480

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 15,162,480 by 2

15,162,480 ÷ 2 = 7,581,240 - No remainder! 2 is one of the factors!
7,581,240 ÷ 2 = 3,790,620 - No remainder! 2 is one of the factors!
3,790,620 ÷ 2 = 1,895,310 - No remainder! 2 is one of the factors!
1,895,310 ÷ 2 = 947,655 - No remainder! 2 is one of the factors!
947,655 ÷ 2 = 473,827.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
947,655 ÷ 3 = 315,885 - No remainder! 3 is one of the factors!
315,885 ÷ 3 = 105,295 - No remainder! 3 is one of the factors!
105,295 ÷ 3 = 35,098.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
105,295 ÷ 5 = 21,059 - No remainder! 5 is one of the factors!
21,059 ÷ 5 = 4,211.8 - There is a remainder. We can't divide by 5 evenly anymore. Let's try the next prime number
21,059 ÷ 7 = 3,008.4286 - This has a remainder. 7 is not a factor.
21,059 ÷ 11 = 1,914.4545 - This has a remainder. 11 is not a factor.
21,059 ÷ 13 = 1,619.9231 - This has a remainder. 13 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
21,059 ÷ 21,059 = 1 - No remainder! 21,059 is one of the factors!

The orange divisor(s) above are the prime factors of the number 15,162,480. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 3 x 3 x 5 x 21,059 = 15,162,480. It can also be written in exponential form as 24 x 32 x 51 x 21,0591.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 15,162,480.

15,162,480
Factor Arrows
27,581,240
Factor Arrows
23,790,620
Factor Arrows
21,895,310
Factor Arrows
2947,655
Factor Arrows
3315,885
Factor Arrows
3105,295
Factor Arrows
521,059

More Prime Factorization Examples

15,162,47815,162,47915,162,48115,162,482
21 x 1,4811 x 5,11912811 x 53,959115,162,481121 x 471 x 161,3031

Try the factor calculator

Explore more about the number 15,162,480:


Ask a Question