Question

Find the sum of factors of 11760​

Answer 1

$\huge\bf{Given::}$

Find the sum of factors of 11760

$\huge\bf{Solution::}$

Factors of 11760 in 2 pairs :

• 1 × 11760 = 11760
• 2 × 5880 = 11760
• 3 × 3920 = 11760
• 4 × 2940 = 11760
• 5 × 2352 = 11760
• 6 × 1960 = 11760
• 7 × 1680 = 11760
• 8 × 1470 = 11760
• 10 × 1176 = 11760
• 12 × 980 = 11760
• 14 × 840 = 11760
• 15 × 784 = 11760
• 16 × 735 = 11760
• 20 × 588 = 11760
• 21 × 560 = 11760
• 24 × 490 = 11760
• 28 × 420 = 11760
• 30 × 392 = 11760
• 35 × 336 = 11760
• 40 × 294 = 11760
• 42 × 280 = 11760
• 48 × 245 = 11760
• 49 × 240 = 11760
• 56 × 210 = 11760
• 60 × 196 = 11760
• 70 × 168 = 11760
• 80 × 147 = 11760
• 84 × 140 = 11760
• 98 × 120 = 11760
• 105 × 112 = 11760
• 112 × 105 = 11760
• 120 × 98 = 11760
• 140 × 84 = 11760
• 147 × 80 = 11760
• 168 × 70 = 11760
• 196 × 60 = 11760
• 210 × 56 = 11760
• 240 × 49 = 11760
• 245 × 48 = 11760
• 280 × 42 = 11760
• 294 × 40 = 11760
• 336 × 35 = 11760
• 392 × 30 = 11760
• 420 × 28 = 11760
• 490 × 24 = 11760
• 560 × 21 = 11760
• 588 × 20 = 11760
• 735 × 16 = 11760
• 784 × 15 = 11760
• 840 × 14 = 11760
• 980 × 12 = 11760
• 1176 × 10 = 11760
• 1470 × 8 = 11760
• 1680 × 7 = 11760
• 1960 × 6 = 11760
• 2352 × 5 = 11760
• 2940 × 4 = 11760
• 3920 × 3 = 11760
• 5880 × 2 = 11760
• 11760 × 1 = 11760

So, the factors of 11760 will be :

• 1
• 2
• 3
• 4
• 5
• 6
• 7
• 8
• 10
• 12
• 14
• 15
• 16
• 20
• 21
• 24
• 28
• 30
• 35
• 40
• 42
• 48
• 49
• 56
• 60
• 70
• 80
• 84
• 98
• 105
• 112
• 120
• 140
• 147
• 168
• 196
• 210
• 240
• 245
• 280
• 294
• 336
• 392
• 420
• 490
• 560
• 588
• 735
• 784
• 840
• 980
• 1176
• 1470
• 1680
• 1960
• 2352
• 2940
• 3920
• 5880

Sum of all factors :

1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 10 + 12 + 14 + 15 + 16 + 20 + 21 + 24 + 28 + 30 + 35 + 40 + 42 + 48 + 49 + 56 + 60 + 70 + 80 + 84 + 98 + 105 + 112 + 120 + 140 + 147 + 168 + 196 + 210 + 240 + 245 + 280 + 294 + 336 + 392 + 420 + 490 + 560 + 588 + 735 + 784 + 840 + 980 + 1176 + 1470 + 1680 + 1960 + 2352 + 2940 + 3920 + 5880 = 30648 ans

$\huge\bf{Additional \: Info::}$

How to find factors of a number :

Let's take an example and find the factors of 16.

Step 1: Write the numbers from 1 to 16

1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16

Step 2: Check now, which number can divide the 16 equally from the above list of numbers.

• 16/1 = 16

• 16/2 = 8

• 16/3 = fraction

In the same way, divide 16 by each of these numbers.

Step 3: Hence, we get the factors of 16 are 1, 2, 4, 8, and 16

Prime Factorization of 11760 :

$\begin{array}{c | l}2 & 11760 \\\hline 2 & 5880 \\\hline 2 & 2940 \\\hline 2 & 1470 \\\hline 5 & 735 \\\hline 7 & 147 \\\hline 7 & 21 \\\hline 3 & 3 \\\hline & 1 \\\end{array}$

Prime Factors of 11760 = 2, 2, 2, 2, 3, 5, 7, 7

$\large\bf{Hope \: it \: helps}$