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Question

Find the prime factorization of number 784.

Answer

The prime factorization of 784 is:

$$ 784 = 2\cdot2\cdot2\cdot2\cdot7\cdot7 $$

Which is the same as :

$$ 784 = 2^{4}\cdot7^{2} $$

Explanation

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

784 can be written as 2 × 392.
  • 784
    • 2
    • 392
392 can be written as 2 × 196.
  • 784
    • 2
    • 392
      • 196
      • 2
196 can be written as 2 × 98.
  • 784
    • 2
    • 392
      • 196
        • 2
        • 98
      • 2
98 can be written as 2 × 49.
  • 784
    • 2
    • 392
      • 196
        • 2
        • 98
          • 49
          • 2
      • 2
49 can be written as 7 × 7.
  • 784
    • 2
    • 392
      • 196
        • 2
        • 98
          • 49
            • 7
            • 7
          • 2
      • 2
The end nodes are the prime factors of the number 784.
  • 784
    • 2
    • 392
      • 196
        • 2
        • 98
          • 49
            • 7
            • 7
          • 2
      • 2
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Prime factorization calculator