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# Primes and Perfect Squares

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A natural number greater than 1 is said to be prime if its only factors are 1 and itself. For example, the number 7 is prime since its only factors are 1 and 7. A perfect square is an integer created by multiplying an integer by itself. The number 25 is a perfect square since it is 5 × 5 or 5 Determine the smallest perfect square that has three different prime numbers as factors.

Guest Jan 17, 2016

#1
+18715
+30

A natural number greater than 1 is said to be prime if its only factors are 1 and itself. For example, the number 7 is prime since its only factors are 1 and 7. A perfect square is an integer created by multiplying an integer by itself. The number 25 is a perfect square since it is 5 × 5 or 5 Determine the smallest perfect square that has three different prime numbers as factors.

$$(2 \cdot 3\cdot 5)^2 = 2^2\cdot 3^2\cdot 5^2 = 4\cdot 9\cdot 25 =\mathbf{ 900}$$

heureka  Jan 18, 2016
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#1
+18715
+30

A natural number greater than 1 is said to be prime if its only factors are 1 and itself. For example, the number 7 is prime since its only factors are 1 and 7. A perfect square is an integer created by multiplying an integer by itself. The number 25 is a perfect square since it is 5 × 5 or 5 Determine the smallest perfect square that has three different prime numbers as factors.

$$(2 \cdot 3\cdot 5)^2 = 2^2\cdot 3^2\cdot 5^2 = 4\cdot 9\cdot 25 =\mathbf{ 900}$$

heureka  Jan 18, 2016

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