By what number should be 86700 divided to make it a perfect square?

Answer: Divide by 3.

Reason:

• Factorize 86700: 86700 = 867 × 100 = (3 × 17^2) × (2^2 × 5^2) = 2^2 · 3 · 5^2 · 17^2.

• For a number to be a perfect square, every prime exponent must be even. Here, the exponents are: 2→2, 3→1, 5→2, 17→2. Only the exponent of 3 is odd.

• Remove the single factor of 3 by dividing by 3: 86700 ÷ 3 = 28900.

• Check: 28900 = 289 × 100 = 17^2 × 10^2 = (17×10)^2 = 170^2, which is a perfect square.

• Therefore, dividing 86700 by 3 makes it a perfect square.