Is 5760 an abundant number and what is its abundance?

Is 5760 an abundant number?

Here we will explain and calculate if 5760 is an abundant number and its abundance if applicable.

5760 is an abundant number if the sum of its proper divisors is greater than 5760.

The sum of its proper divisors is calculated as follows: 1 + 2 + 3 + 4 + 5 + 6 + 8 + 9 + 10 + 12 + 15 + 16 + 18 + 20 + 24 + 30 + 32 + 36 + 40 + 45 + 48 + 60 + 64 + 72 + 80 + 90 + 96 + 120 + 128 + 144 + 160 + 180 + 192 + 240 + 288 + 320 + 360 + 384 + 480 + 576 + 640 + 720 + 960 + 1152 + 1440 + 1920 + 2880 = 14130.

14130 is greater than 5760. Therefore, 5760 is an abundant number.

The abundance of 5760 is the sum of its proper divisors minus 5760. Thus, the abundance of 5760 is 14130 - 5760 = 8370

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