Q: What is the prime factorization of the number 88,017,408?

 A:
  • The prime factors are: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 6,367
    • or also written as { 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 6,367 }
  • Written in exponential form: 29 x 33 x 6,3671

Why is the prime factorization of 88,017,408 written as 29 x 33 x 6,3671?

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 88,017,408

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 88,017,408 by 2

88,017,408 ÷ 2 = 44,008,704 - No remainder! 2 is one of the factors!
44,008,704 ÷ 2 = 22,004,352 - No remainder! 2 is one of the factors!
22,004,352 ÷ 2 = 11,002,176 - No remainder! 2 is one of the factors!
11,002,176 ÷ 2 = 5,501,088 - No remainder! 2 is one of the factors!
5,501,088 ÷ 2 = 2,750,544 - No remainder! 2 is one of the factors!
2,750,544 ÷ 2 = 1,375,272 - No remainder! 2 is one of the factors!
1,375,272 ÷ 2 = 687,636 - No remainder! 2 is one of the factors!
687,636 ÷ 2 = 343,818 - No remainder! 2 is one of the factors!
343,818 ÷ 2 = 171,909 - No remainder! 2 is one of the factors!
171,909 ÷ 2 = 85,954.5 - There is a remainder. We can't divide by 2 evenly anymore. Let's try the next prime number
171,909 ÷ 3 = 57,303 - No remainder! 3 is one of the factors!
57,303 ÷ 3 = 19,101 - No remainder! 3 is one of the factors!
19,101 ÷ 3 = 6,367 - No remainder! 3 is one of the factors!
6,367 ÷ 3 = 2,122.3333 - There is a remainder. We can't divide by 3 evenly anymore. Let's try the next prime number
6,367 ÷ 5 = 1,273.4 - This has a remainder. 5 is not a factor.
6,367 ÷ 7 = 909.5714 - This has a remainder. 7 is not a factor.
6,367 ÷ 11 = 578.8182 - This has a remainder. 11 is not a factor.
...
Keep trying increasingly larger numbers until you find one that divides evenly.
...
6,367 ÷ 6,367 = 1 - No remainder! 6,367 is one of the factors!

The orange divisor(s) above are the prime factors of the number 88,017,408. 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 3 x 3 x 3 x 6,367 = 88,017,408. It can also be written in exponential form as 29 x 33 x 6,3671.

Factor Tree

Another way to do prime factorization is to use a factor tree. Below is a factor tree for the number 88,017,408.

88,017,408
Factor Arrows
244,008,704
Factor Arrows
222,004,352
Factor Arrows
211,002,176
Factor Arrows
25,501,088
Factor Arrows
22,750,544
Factor Arrows
21,375,272
Factor Arrows
2687,636
Factor Arrows
2343,818
Factor Arrows
2171,909
Factor Arrows
357,303
Factor Arrows
319,101
Factor Arrows
36,367

More Prime Factorization Examples

88,017,40688,017,40788,017,40988,017,410
21 x 411 x 1,073,3831291 x 3,035,08315,7911 x 15,199121 x 51 x 131 x 677,0571

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