In how many ways can 144 be written as product of two of its distinct factors?
Explanation:
Number of ways of writing a perfect square as a product of two of its distinct factors is equal to half the (number of its factors - 1). Here 144 is a perfect square.
144 = 24 × 32
Number of factors of 144 = (4 + 1)(2 + 1) = 15
Number of ways of writing a perfect square as a product of two of its distinct factors = ½ × (15 - 1) = 7
[1×144, 2×72, 3×48, 4×36, 6×24, 8×18, 9×16]
Hence, 7.
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