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5328 prime factorization

What is the prime factorization of 5328?

Find the prime factorization of 5328

We draw a vertical line and write 5328 to the left of the line:

5328  

5328 is divisible by 9

5328 : 9 =
5328 : (3 * 3) = 592

We write (3 * 3) (the divisor) to the right of the line and 592 to the left of the line:

5328  3 * 3
 592  

3 is a prime number.

592 is not a prime number.

See Prime numbers 1 through 1000.

592 is divisible by 4

592 : 4 =
592 : (2 * 2) = 148

We write (2 * 2) (the divisor) to the right of the line and 148 to the left of the line:

5328  3 * 3
 592  2 * 2
 148  

148 is divisible by 4

148 : 4 =
148 : (2 * 2) = 37

We write (2 * 2) (the divisor) to the right of the line and 37 to the left of the line:

5328  3 * 3
 592  2 * 2
 148  2 * 2
  37  

37 is a prime number. 37 is divisible by itself and by 1. We divide 37 by 37:

37 : 37 = 1

and write 37 (the divisor) to the right of the line and 1 to the left of the line:

5328  3 * 3
 592  2 * 2
 148  2 * 2
  37  37
   1 

The numbers to the right of the line are prime factors of the number 5328.

Therefore, the prime factorization of 5328 is

5328 =
2 * 2 * 2 * 2 * 3 * 3 * 37

The prime factorization of 5328 using exponents

5328 =
24 * 32 * 37

So, the prime factors of 5328 are

2, 2, 2, 2, 3, 3, 37