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213444 prime factorization

What is the prime factorization of 213444?

Find the prime factorization of 213444

We draw a vertical line and write 213444 to the left of the line:

213444  

213444 is divisible by 9

213444 : 9 =
213444 : (3 * 3) = 23716

We write (3 * 3) (the divisor) to the right of the line and 23716 to the left of the line:

213444  3 * 3
 23716  

3 is a prime number.

See Prime numbers 1 through 20.

23716 is not a prime number.

23716 is divisible by 7

23716 : 7 = 3388

We write 7 (the divisor) to the right of the line and 3388 to the left of the line:

213444  3 * 3
 23716  7
  3388  

3388 is divisible by 11:

3388 : 11 = 308

We write 11 (the divisor) to the right of the line and 308 to the left of the line:

213444  3 * 3
 23716  7
  3388  11
   308  

308 is divisible by 11:

308 : 11 = 28

We write 11 (the divisor) to the right of the line and 28 to the left of the line:

213444  3 * 3
 23716  7
  3388  11
   308  11
    28  

28 is divisible by 4:

28 : 4 = 28 : (2 * 2) = 7

We write (2 * 2) (the divisor) to the right of the line and 7 to the left of the line:

213444  3 * 3
 23716  7
  3388  11
   308  11
    28  2 * 2
     7  

7 is a prime number. 7 is divisible by itself and by 1. We divide 7 by 7:

7 : 7 = 1

and write 7 (the divisor) to the right of the line and 1 to the left of the line:

213444  3 * 3
 23716  7
  3388  11
   308  11
    28  2 * 2
     7  7
     1 

The numbers to the right of the line are prime factors of the number 213444.

Therefore, the prime factorization of 213444 is

213444 =
2 * 2 * 3 * 3 * 7 * 7 * 11 * 11

The prime factorization of 213444 using exponents

213444 =
22 * 32 * 72 * 112

So, the prime factors of 213444 are

2, 2, 3, 3, 7, 7, 11, 11