GB-09-05-001 · Square numbers from prime factors

Find the smallest positive integer $k$ such that $900k$ is a square number.

Prime Factors & Square Numbers Booklet p. 42

Method

1) Write number in prime factor index form

2) For a square number every prime power must be even; multiply by primes with odd powers

Worked Example (GB-09-05-001)

900

450

225

In a square, every prime exponent is even.

900=2^{2}\times3^{2}\times5^{2}

Every exponent is already even, so the smallest positive k is 1.

Ans = 1