Hampton Vaughan
05/10/2024 · High School
Determine whether this statement is true or false: A perfect square will always have an odd number of factors. Tentukan sama ada pernyataan berikut benar atau salah: Bilangan faktor bagi suatu kuasa dua sempurna adalah sentiasa ganjil True / Benar False / Salah
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The statement is **True** / **Benar**.
A perfect square has an odd number of factors because the factors can be paired up except for the square root, which is counted only once. For example, if \( n \) is a perfect square, say \( n = k^2 \), the factors of \( n \) can be expressed in pairs \( (d, \frac{n}{d}) \). The only factor that does not have a distinct pair is \( k \) itself, which results in an odd count of total factors.
Therefore, the statement that a perfect square will always have an odd number of factors is true.
Quick Answer
True / Benar
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