Is There A Pattern To It?

Number Theory Level pending

\[ \large \underbrace1_{\text{odd}}, \underbrace2_{\text{even}}, \underbrace3_{\text{odd}}, \underbrace4_{\text{even}}, \underbrace5_{\text{odd}}, \underbrace{6}_{\text{even}}, \underbrace{8}_{\text{even}}, \underbrace9_{\text{odd}}, \underbrace{10}_{\text{even}},\underbrace{12}_{\text{even}},\underbrace{15}_{\text{odd}} , \ldots \]

Above shows an incomplete list of factors of the number 1440, some of these factors are odd and some are even. How many of these factors are even?

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