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Question

Find the prime factorization of number 282475249.

Answer

The prime factorization of 282475249 is:

$$ 282475249 = 7\cdot7\cdot7\cdot7\cdot7\cdot7\cdot7\cdot7\cdot7\cdot7 $$

Which is the same as :

$$ 282475249 = 7^{10} $$

Explanation

Prime factorization can be nicely visualized by creating a factorization tree.

282475249 can be written as 7 × 40353607.
  • 282475249
    • 7
    • 40353607
40353607 can be written as 7 × 5764801.
  • 282475249
    • 7
    • 40353607
      • 5764801
      • 7
5764801 can be written as 7 × 823543.
  • 282475249
    • 7
    • 40353607
      • 5764801
        • 7
        • 823543
      • 7
823543 can be written as 7 × 117649.
  • 282475249
    • 7
    • 40353607
      • 5764801
        • 7
        • 823543
          • 117649
          • 7
      • 7
117649 can be written as 7 × 16807.
  • 282475249
    • 7
    • 40353607
      • 5764801
        • 7
        • 823543
          • 117649
            • 7
            • 16807
          • 7
      • 7
16807 can be written as 7 × 2401.
  • 282475249
    • 7
    • 40353607
      • 5764801
        • 7
        • 823543
          • 117649
            • 7
            • 16807
              • 2401
              • 7
          • 7
      • 7
2401 can be written as 7 × 343.
  • 282475249
    • 7
    • 40353607
      • 5764801
        • 7
        • 823543
          • 117649
            • 7
            • 16807
              • 2401
                • 7
                • 343
              • 7
          • 7
      • 7
343 can be written as 7 × 49.
  • 282475249
    • 7
    • 40353607
      • 5764801
        • 7
        • 823543
          • 117649
            • 7
            • 16807
              • 2401
                • 7
                • 343
                  • 49
                  • 7
              • 7
          • 7
      • 7
49 can be written as 7 × 7.
  • 282475249
    • 7
    • 40353607
      • 5764801
        • 7
        • 823543
          • 117649
            • 7
            • 16807
              • 2401
                • 7
                • 343
                  • 49
                    • 7
                    • 7
                  • 7
              • 7
          • 7
      • 7
The end nodes are the prime factors of the number 282475249.
  • 282475249
    • 7
    • 40353607
      • 5764801
        • 7
        • 823543
          • 117649
            • 7
            • 16807
              • 2401
                • 7
                • 343
                  • 49
                    • 7
                    • 7
                  • 7
              • 7
          • 7
      • 7
This page was created using
Prime factorization calculator