What is the prime factorization of the number 1728?

Prime factors of 1728

The prime factors are: 2, 2, 2, 2, 2, 2, 3, 3, 3
Prime Factor Decomposition or Prime Factorization is the process of finding which prime numbers can be multiplied together to make the original number. 1728 divided by 2, 2, 2, 2, 2, 2, 3, 3, 3 gives no remainder. This means Prime number are numbers that can divide without remainder.

How to Calculate Prime Factorization of 1728?

The main method of prime factorization is start dividing the number by the any divisible prime numbers until the only numbers left are prime numbers \( (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, ...) \).

\(1728\div \color{red}{2} = 864\)
\(864\div \color{red}{2} = 432\)
\(432\div \color{red}{2} = 216\)
\(216\div \color{red}{2} = 108\)
\(108\div \color{red}{2} = 54\)
\(54\div \color{red}{2} = 27\)
\(27\div \color{red}{3} = 9\)
\(9\div \color{red}{3} = 3\)
\(3\div \color{red}{3} = 1\)

Factorize\( (1728) = \) \(2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 3\)

Factor Tree of 1728

	1728
2		864
	2		432
		2		216
			2		108
				2		54
					2		27
						3		9
							3		3

If you want to learn more about prime factorization, take a look at the Wikipedia page.

Prime factors of:

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