Q: What is the prime factorization of the number 83,820,544?

 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 2 x 2 x 2 x 2 x 1,279
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1,279 }
  • Written in exponential form: 216 x 1,2791

Why is the prime factorization of 83,820,544 written as 216 x 1,2791?

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 83,820,544

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 83,820,544 by 2

83,820,544 ÷ 2 = 41,910,272 - No remainder! 2 is one of the factors!
41,910,272 ÷ 2 = 20,955,136 - No remainder! 2 is one of the factors!
20,955,136 ÷ 2 = 10,477,568 - No remainder! 2 is one of the factors!
10,477,568 ÷ 2 = 5,238,784 - No remainder! 2 is one of the factors!
5,238,784 ÷ 2 = 2,619,392 - No remainder! 2 is one of the factors!
2,619,392 ÷ 2 = 1,309,696 - No remainder! 2 is one of the factors!
1,309,696 ÷ 2 = 654,848 - No remainder! 2 is one of the factors!
654,848 ÷ 2 = 327,424 - No remainder! 2 is one of the factors!
327,424 ÷ 2 = 163,712 - No remainder! 2 is one of the factors!
163,712 ÷ 2 = 81,856 - No remainder! 2 is one of the factors!
81,856 ÷ 2 = 40,928 - No remainder! 2 is one of the factors!
40,928 ÷ 2 = 20,464 - No remainder! 2 is one of the factors!
20,464 ÷ 2 = 10,232 - No remainder! 2 is one of the factors!
10,232 ÷ 2 = 5,116 - No remainder! 2 is one of the factors!
5,116 ÷ 2 = 2,558 - No remainder! 2 is one of the factors!
2,558 ÷ 2 = 1,279 - No remainder! 2 is one of the factors!
1,279 ÷ 2 = 639.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
1,279 ÷ 3 = 426.3333 - This has a remainder. 3 is not a factor.
1,279 ÷ 5 = 255.8 - This has a remainder. 5 is not a factor.
1,279 ÷ 7 = 182.7143 - This has a remainder. 7 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
1,279 ÷ 1,279 = 1 - No remainder! 1,279 is one of the factors!

The orange divisor(s) above are the prime factors of the number 83,820,544. 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 2 x 2 x 2 x 2 x 1,279 = 83,820,544. It can also be written in exponential form as 216 x 1,2791.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 83,820,544.

83,820,544
Factor Arrows
241,910,272
Factor Arrows
220,955,136
Factor Arrows
210,477,568
Factor Arrows
25,238,784
Factor Arrows
22,619,392
Factor Arrows
21,309,696
Factor Arrows
2654,848
Factor Arrows
2327,424
Factor Arrows
2163,712
Factor Arrows
281,856
Factor Arrows
240,928
Factor Arrows
220,464
Factor Arrows
210,232
Factor Arrows
25,116
Factor Arrows
22,558
Factor Arrows
21,279

More Prime Factorization Examples

83,820,54283,820,54383,820,54583,820,546
21 x 131 x 3,223,867131 x 27,940,181151 x 431 x 1971 x 1,979121 x 32 x 1491 x 31,2531

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