What is the prime factorization of the number 30976?

Prime factors of 30976

The prime factors are: 2, 2, 2, 2, 2, 2, 2, 2, 11, 11
Prime Factor Decomposition or Prime Factorization is the process of finding which prime numbers can be multiplied together to make the original number. 30976 divided by 2, 2, 2, 2, 2, 2, 2, 2, 11, 11 gives no remainder. This means Prime number are numbers that can divide without remainder.

How to Calculate Prime Factorization of 30976?

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

\(30976\div \color{red}{2} = 15488\)
\(15488\div \color{red}{2} = 7744\)
\(7744\div \color{red}{2} = 3872\)
\(3872\div \color{red}{2} = 1936\)
\(1936\div \color{red}{2} = 968\)
\(968\div \color{red}{2} = 484\)
\(484\div \color{red}{2} = 242\)
\(242\div \color{red}{2} = 121\)
\(121\div \color{red}{11} = 11\)
\(11\div \color{red}{11} = 1\)

Factorize\( (30976) = \) \(2\times 2\times 2\times 2\times 2\times 2\times 2\times 2\times 11\times 11\)

Factor Tree of 30976

	30976
2		15488
	2		7744
		2		3872
			2		1936
				2		968
					2		484
						2		242
							2		121
								11		11

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

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