What is the prime factorization of 289?

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To calculate the prime factors of 289 enter a number in the field below and press decompose:

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Answer to the Factorization of 289

The factorization of 289 is equal to 17 × 17. We find these factors by successively dividing 289 by the prime numbers until we obtain the prime factors.

Factor Tree of 289

The prime factor tree of 289 is an illustration that shows how the number 289 is decomposed into its fundamental prime factors, as 2, 3 and 5. This visual representation helps you understand the underlying structure of the number and how it is formed from smaller prime numbers.

Look at the following tree:

17 17
17 1

Steps to Factor the Number 289

1. Division by Smaller Prime Numbers:

Start by dividing the number 289 by the smallest prime numbers, starting with the smallest prime, which is 17.

289 ÷ 17 = 17

2. Obtaining Prime Factors:

Now, the numbers by which you divided 289 and got integer results are the prime factors of 289. In this case, we have 17 and 17.

3. Factorization Expression:

Write the factorization of the number 289 using its prime factors. The full factorization of 289 is:

289 = 17 × 17

These steps show how the number 289 can be factored into its prime components, which is helpful in understanding its structure and mathematical properties.

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