No, not every number has an even number of factors. Most numbers do, but perfect square numbers have an odd number of factors because one factor (like 6 in 36) is repeated and does not pair with a different number.
Class 8 Mathematics Ganita Prakash A Square and A Cube
Class 8 Mathematics Ganita Prakash Chapter 1 A Square and A Cube NCERT solutions
Most numbers have an even number of factors, as they come in factor pairs. For example, 6 has 1×6 and 2×3. However, perfect square numbers like 36 have one repeated factor (6×6), making the total number of factors odd. So, only perfect squares have an odd number of factors. This property is key to solving the locker puzzle and understanding which lockers stay open.
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