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What is the smallest value of k when 882k is a cube?
To find the smallest value of k when 882k is a cube, we need to factor out the cube from 882k. The prime factorization of 882 is 2 x 3^2 x 7^2. For 882k to be a cube, we need to find the smallest value of k such that the exponent of each prime factor in the prime factorization of 882k is a multiple of 3. Therefore, the smallest value of k would be 2^2 x 3 x 7 = 84.
What are the first 4 cube numbers that are also multiples of 3?
33 = 81 63 = 216 93 = 729 and 123 = 1728
The cube root of this number is one more than the smallest prime?
The cube root of this number is one more than the smallest prime
What is the smallest integer k such that 756k is a perfect cube?
k = 98. In the prime factorization (in power format) of a perfect cube, every prime must be to the power of a multiple of 3. 756 = 2^2 x 3^3 x 7 Thus the smallest perfect cube that is a multiple of 756 is 2^3 × 3^3 × 7^3; to obtain this need to multiply 756 by 2^1 × 3^0 × 7^2 = 98 Thus the smallest k to make 756k a perfect prime is k = 98.
Which 1-digit number is neither a prime nor a square nor a cube?
6
