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Select the option that does NOT belong to the same category as the others: 343, 512, 2197, 1331
343
512
2197
1331
512
Identify if numbers are cubes of prime numbers or composite numbers. All options are cubes, but only one is a cube of an even number.
Identify if numbers are cubes of prime numbers or composite numbers. All options are cubes, but only one is a cube of an even number.
Analyze the mathematical property of each number
343 is 7 cubed (777). 512 is 8 cubed (888). 2197 is 13 cubed (131313). 1331 is 11 cubed (111111).
Identify the base numbers
The base numbers are 7, 8, 13, and 11. Among these, 7, 13, and 11 are prime numbers, whereas 8 is a composite number (even number).
A: 343 is 7 cubed and 7 is a prime number, thus it shares the same category as C and D. C: 2197 is 13 cubed and 13 is a prime number, fitting the category. D: 1331 is 11 cubed and 11 is a prime number, fitting the category.
B is correct because 512 is the cube of 8, which is an even composite number, whereas 343, 2197, and 1331 are cubes of odd prime numbers.
In number classification, always check for prime/composite properties of bases if all given numbers are perfect powers (squares or cubes).
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