Q: What is the prime factorization of the number 53,312,464?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 41 x 181 x 449
    • or also written as { 2, 2, 2, 2, 41, 181, 449 }
  • Written in exponential form: 24 x 411 x 1811 x 4491

Why is the prime factorization of 53,312,464 written as 24 x 411 x 1811 x 4491?

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 53,312,464

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 53,312,464 by 2

53,312,464 ÷ 2 = 26,656,232 - No remainder! 2 is one of the factors!
26,656,232 ÷ 2 = 13,328,116 - No remainder! 2 is one of the factors!
13,328,116 ÷ 2 = 6,664,058 - No remainder! 2 is one of the factors!
6,664,058 ÷ 2 = 3,332,029 - No remainder! 2 is one of the factors!
3,332,029 ÷ 2 = 1,666,014.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
3,332,029 ÷ 3 = 1,110,676.3333 - This has a remainder. 3 is not a factor.
3,332,029 ÷ 5 = 666,405.8 - This has a remainder. 5 is not a factor.
3,332,029 ÷ 7 = 476,004.1429 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
3,332,029 ÷ 41 = 81,269 - No remainder! 41 is one of the factors!
81,269 ÷ 41 = 1,982.1707 - There is a remainder. We can't divide by 41 evenly anymore. Let's try the next prime number
81,269 ÷ 43 = 1,889.9767 - This has a remainder. 43 is not a factor.
81,269 ÷ 47 = 1,729.1277 - This has a remainder. 47 is not a factor.
81,269 ÷ 53 = 1,533.3774 - This has a remainder. 53 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
81,269 ÷ 181 = 449 - No remainder! 181 is one of the factors!
449 ÷ 181 = 2.4807 - There is a remainder. We can't divide by 181 evenly anymore. Let's try the next prime number
449 ÷ 191 = 2.3508 - This has a remainder. 191 is not a factor.
449 ÷ 193 = 2.3264 - This has a remainder. 193 is not a factor.
449 ÷ 197 = 2.2792 - This has a remainder. 197 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
449 ÷ 449 = 1 - No remainder! 449 is one of the factors!

The orange divisor(s) above are the prime factors of the number 53,312,464. If we put all of it together we have the factors 2 x 2 x 2 x 2 x 41 x 181 x 449 = 53,312,464. It can also be written in exponential form as 24 x 411 x 1811 x 4491.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 53,312,464.

53,312,464
Factor Arrows
226,656,232
Factor Arrows
213,328,116
Factor Arrows
26,664,058
Factor Arrows
23,332,029
Factor Arrows
4181,269
Factor Arrows
181449

More Prime Factorization Examples

53,312,46253,312,46353,312,46553,312,466
21 x 71 x 3,808,033132 x 7691 x 7,703151 x 1791 x 59,567121 x 31 x 8,885,4111

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