Is 5040 an abundant number and what is its abundance?

Is 5040 an abundant number?

Here we will explain and calculate if 5040 is an abundant number and its abundance if applicable.

5040 is an abundant number if the sum of its proper divisors is greater than 5040.

The sum of its proper divisors is calculated as follows: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18 + 20 + 21 + 24 + 28 + 30 + 35 + 36 + 40 + 42 + 45 + 48 + 56 + 60 + 63 + 70 + 72 + 80 + 84 + 90 + 105 + 112 + 120 + 126 + 140 + 144 + 168 + 180 + 210 + 240 + 252 + 280 + 315 + 336 + 360 + 420 + 504 + 560 + 630 + 720 + 840 + 1008 + 1260 + 1680 + 2520 = 14304.

14304 is greater than 5040. Therefore, 5040 is an abundant number.

The abundance of 5040 is the sum of its proper divisors minus 5040. Thus, the abundance of 5040 is 14304 - 5040 = 9264

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