Express 462 as a product of primes?

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They are: 462, 231, 154, 77, 66, 42, 33, 22, 21, 14, 11, 7, 6, 3, 2, 1. These are all the factors of 462, and every entry in the list can divide 462 without rest (modulo 0). That's why the terms factors and divisors of 462 can be used interchangeably.

As is the case for any natural number greater than zero, the number itself, here 462, as well as 1 are factors and divisors of 462.

Prime Factorization of 462

The prime factorization of 462 is 2 x 3 x 7 x 11. This is a unique list of the prime factors, along with their multiplicities. Note that the prime factorization of 462 does not include the number 1, yet it does include every instance of a certain prime factor.

462 is a composite number. In contrast to prime numbers which only have one factorization, composite numbers like 462 have at least two factorizations.

To illustrate what that means select the rightmost and leftmost integer in 462, 231, 154, 77, 66, 42, 33, 22, 21, 14, 11, 7, 6, 3, 2, 1 and multiply these integers to obtain 462. This is the first factorization. Next choose the second rightmost and the second leftmost entry to obtain the 2nd factorization which also produces 462.

The prime factorization or integer factorization of 462 means determining the set of prime numbers which, when multiplied together, produce the original number 462. This is also known as prime decomposition of 462.


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