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Three distinct prime factors, eight total.
Oh, dude, let me break it down for you. So, 7800 is 2^3 * 3 * 5^2 * 13. To make it a square number, each prime factor needs to appear an even number of times. So, the smallest number it must be multiplied by is 2 * 5 * 13, which is 130. Easy peasy lemon squeezy!
To determine the least number that must be multiplied to 21168 to make it a perfect square, we first find its prime factorization: (21168 = 2^4 \times 3^1 \times 11^1). For a number to be a perfect square, all the exponents in its prime factorization must be even. Here, the exponent of 3 and 11 are odd, so we need at least one more factor of each. Thus, we multiply by (3^1 \times 11^1 = 33). Therefore, the least number that must be multiplied to 21168 to make it a perfect square is 33.
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No. A prime number must, itself, be a natural number.No. A prime number must, itself, be a natural number.No. A prime number must, itself, be a natural number.No. A prime number must, itself, be a natural number.