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Question

Find the prime factorization of number 117649.

Answer

The prime factorization of 117649 is:

$$ 117649 = 7\cdot7\cdot7\cdot7\cdot7\cdot7 $$

Which is the same as :

$$ 117649 = 7^{6} $$

Explanation

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

117649 can be written as 7 × 16807.
  • 117649
    • 7
    • 16807
16807 can be written as 7 × 2401.
  • 117649
    • 7
    • 16807
      • 2401
      • 7
2401 can be written as 7 × 343.
  • 117649
    • 7
    • 16807
      • 2401
        • 7
        • 343
      • 7
343 can be written as 7 × 49.
  • 117649
    • 7
    • 16807
      • 2401
        • 7
        • 343
          • 49
          • 7
      • 7
49 can be written as 7 × 7.
  • 117649
    • 7
    • 16807
      • 2401
        • 7
        • 343
          • 49
            • 7
            • 7
          • 7
      • 7
The end nodes are the prime factors of the number 117649.
  • 117649
    • 7
    • 16807
      • 2401
        • 7
        • 343
          • 49
            • 7
            • 7
          • 7
      • 7
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