What is the prime factorization of the number 6400?

Prime factors of 6400

The prime factors are: 2, 2, 2, 2, 2, 2, 2, 2, 5, 5
Prime Factor Decomposition or Prime Factorization is the process of finding which prime numbers can be multiplied together to make the original number. 6400 divided by 2, 2, 2, 2, 2, 2, 2, 2, 5, 5 gives no remainder. This means Prime number are numbers that can divide without remainder.

How to Calculate Prime Factorization of 6400?

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

\(6400\div \color{red}{2} = 3200\)
\(3200\div \color{red}{2} = 1600\)
\(1600\div \color{red}{2} = 800\)
\(800\div \color{red}{2} = 400\)
\(400\div \color{red}{2} = 200\)
\(200\div \color{red}{2} = 100\)
\(100\div \color{red}{2} = 50\)
\(50\div \color{red}{2} = 25\)
\(25\div \color{red}{5} = 5\)
\(5\div \color{red}{5} = 1\)

Factorize\( (6400) = \) \(2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 5\times 5\)

Factor Tree of 6400

	6400
2		3200
	2		1600
		2		800
			2		400
				2		200
					2		100
						2		50
							2		25
								5		5

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

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