What is the prime factorization of the number 54144?

Prime factors of 54144

The prime factors are: 2, 2, 2, 2, 2, 2, 2, 3, 3, 47
Prime Factor Decomposition or Prime Factorization is the process of finding which prime numbers can be multiplied together to make the original number. 54144 divided by 2, 2, 2, 2, 2, 2, 2, 3, 3, 47 gives no remainder. This means Prime number are numbers that can divide without remainder.

How to Calculate Prime Factorization of 54144?

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 \( (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, ...) \).

\(54144\div \color{red}{2} = 27072\)
\(27072\div \color{red}{2} = 13536\)
\(13536\div \color{red}{2} = 6768\)
\(6768\div \color{red}{2} = 3384\)
\(3384\div \color{red}{2} = 1692\)
\(1692\div \color{red}{2} = 846\)
\(846\div \color{red}{2} = 423\)
\(423\div \color{red}{3} = 141\)
\(141\div \color{red}{3} = 47\)
\(47\div \color{red}{47} = 1\)

Factorize\( (54144) = \) \(2\times 2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 47\)

Factor Tree of 54144

	54144
2		27072
	2		13536
		2		6768
			2		3384
				2		1692
					2		846
						2		423
							3		141
								3		47

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

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