Answer to Question #13156 in Math for rahul kumar

Question

How many integers from 1 to 9999 have exactly 15 divisors?

Answer 1

Integer 144 has 15 divisors
Divisors: 1 2 3 4 6 8 9 12 16 18 24 36 48 72
144
Integer 324 has 15 divisors
Divisors: 1 2 3 4 6 9 12 18 27 36 54 81
108 162 324
Integer 400 has 15 divisors
Divisors: 1 2 4 5 8 10 16 20 25 40
50 80 100 200 400
Integer 784 has 15 divisors
Divisors: 1 2 4 7 8 14 16 28
49 56 98 112 196 392 784
Integer 1936 has 15 divisors
Divisors: 1 2 4 8 11
16 22 44 88 121 176 242 484 968 1936
Integer 2025 has 15
divisors
Divisors: 1 3 5 9 15 25 27 45 75 81 135 225 405 675 2025
Integer
2500 has 15 divisors
Divisors: 1 2 4 5 10 20 25 50 100 125 250 500 625 1250
2500
Integer 2704 has 15 divisors
Divisors: 1 2 4 8 13 16 26 52 104 169
208 338 676 1352 2704
Integer 3969 has 15 divisors
Divisors: 1 3 7 9 21 27
49 63 81 147 189 441 567 1323 3969
Integer 4624 has 15 divisors
Divisors:
1 2 4 8 16 17 34 68 136 272 289 578 1156 2312 4624
Integer 5625 has 15
divisors
Divisors: 1 3 5 9 15 25 45 75 125 225 375 625 1125 1875
5625
Integer 5776 has 15 divisors
Divisors: 1 2 4 8 16 19 38 76 152 304
361 722 1444 2888 5776
Integer 8464 has 15 divisors
Divisors: 1 2 4 8 16
23 46 92 184 368 529 1058 2116 4232 8464
Integer 9604 has 15
divisors
Divisors: 1 2 4 7 14 28 49 98 196 343 686 1372 2401 4802
9604
Integer 9801 has 15 divisors
Divisors: 1 3 9 11 27 33 81 99 121 297
363 891 1089 3267 9801

total: 15 integers have 15 divisors from 1 to
9999