Q: What is the prime factorization of the number 50,300,016?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 3 x 13 x 149 x 541
    • or also written as { 2, 2, 2, 2, 3, 13, 149, 541 }
  • Written in exponential form: 24 x 31 x 131 x 1491 x 5411

Why is the prime factorization of 50,300,016 written as 24 x 31 x 131 x 1491 x 5411?

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 50,300,016

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 50,300,016 by 2

50,300,016 ÷ 2 = 25,150,008 - No remainder! 2 is one of the factors!
25,150,008 ÷ 2 = 12,575,004 - No remainder! 2 is one of the factors!
12,575,004 ÷ 2 = 6,287,502 - No remainder! 2 is one of the factors!
6,287,502 ÷ 2 = 3,143,751 - No remainder! 2 is one of the factors!
3,143,751 ÷ 2 = 1,571,875.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
3,143,751 ÷ 3 = 1,047,917 - No remainder! 3 is one of the factors!
1,047,917 ÷ 3 = 349,305.6667 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
1,047,917 ÷ 5 = 209,583.4 - This has a remainder. 5 is not a factor.
1,047,917 ÷ 7 = 149,702.4286 - This has a remainder. 7 is not a factor.
1,047,917 ÷ 11 = 95,265.1818 - This has a remainder. 11 is not a factor.
1,047,917 ÷ 13 = 80,609 - No remainder! 13 is one of the factors!
80,609 ÷ 13 = 6,200.6923 - There is a remainder. We can't divide by 13 evenly anymore. Let's try the next prime number
80,609 ÷ 17 = 4,741.7059 - This has a remainder. 17 is not a factor.
80,609 ÷ 19 = 4,242.5789 - This has a remainder. 19 is not a factor.
80,609 ÷ 23 = 3,504.7391 - This has a remainder. 23 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
80,609 ÷ 149 = 541 - No remainder! 149 is one of the factors!
541 ÷ 149 = 3.6309 - There is a remainder. We can't divide by 149 evenly anymore. Let's try the next prime number
541 ÷ 151 = 3.5828 - This has a remainder. 151 is not a factor.
541 ÷ 157 = 3.4459 - This has a remainder. 157 is not a factor.
541 ÷ 163 = 3.319 - This has a remainder. 163 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
541 ÷ 541 = 1 - No remainder! 541 is one of the factors!

The orange divisor(s) above are the prime factors of the number 50,300,016. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 3 x 13 x 149 x 541 = 50,300,016. It can also be written in exponential form as 24 x 31 x 131 x 1491 x 5411.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 50,300,016.

50,300,016
Factor Arrows
225,150,008
Factor Arrows
212,575,004
Factor Arrows
26,287,502
Factor Arrows
23,143,751
Factor Arrows
31,047,917
Factor Arrows
1380,609
Factor Arrows
149541

More Prime Factorization Examples

50,300,01450,300,01550,300,01750,300,018
21 x 25,150,007151 x 1,2831 x 7,84114,4471 x 11,311121 x 25,150,0091

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