There is no such number. Any Prime number raised to the third power has exactly four factors. For example, 23 = 8; its factors are 1, 2, 4, 8 (1, 2, 22, 23). Since - as is well-known - there is no largest prime number, there is no largest number that has exactly four factors.
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To find the factors of a number, you first need to split that number into its prime factors. In the case of 15, this produces: 15 = 3x5 The next step is to note that every factor of the number (apart from 1) is the product of any combination of its prime factors. Thus, the factors of 15 are: 1, 3, 5 and 15.
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The number of factors of a number is calculated as the product of the powers of the number written in power format increased by 1. As there are required to be 5 factors, and as 5 is a prime, it can only be achieved if the number has a prime factorisation which is a single prime raised to the 4th power. The smallest prime is 2, and 2⁴ = 16 The next prime is 3, and 3⁴ = 81 which is too big. → the required number is 16 (which has the 5 factors 1, 2, 4, 8, 16).
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