جدول تفكيك الأعداد الصحيحة الغاوسية
التفكيك

| المعيار | العدد الصحيح | العامل |
| --- | --- | --- |
| 2 |  1+i | (p) |
| 4 |  2 |  −i·(1+i)2 |
| 5 |  1+2i   2+i | (p)  (p) |
| 8 |  2+2i |  −i·(1+i)3 |
| 9 |  3 | (p) |
| 10 |  1+3i   3+i |  (1+i)·(2+i)   (1+i)·(2−i) |
| 13 |  2+3i   3+2i | (p)  (p) |
| 16 |  4 |  −(1+i)4 |
| 17 |  1+4i   4+i | (p)  (p) |
| 18 |  3+3i |  (1+i)·3 |
| 20 |  2+4i   4+2i |  (1+i)2·(2−i)   −i·(1+i)2·(2+i) |
| 25 |  3+4i   4+3i   5 |  (2+i)2   i·(2−i)2   (2+i)·(2−i) |
| 26 |  1+5i   5+i |  (1+i)·(3+2i)   (1+i)·(3−2i) |
| 29 |  2+5i   5+2i | (p)  (p) |
| 32 |  4+4i |  −(1+i)5 |
| 34 |  3+5i   5+3i |  (1+i)·(4+i)   (1+i)·(4−i) |
| 36 |  6 |  −i·(1+i)2·3 |
| 37 |  1+6i   6+i | (p)  (p) |
| 40 |  2+6i   6+2i |  −i·(1+i)3·(2+i)   −i·(1+i)3·(2−i) |
| 41 |  4+5i   5+4i | (p)  (p) |
| 45 |  3+6i   6+3i |  i·(2−i)·3   (2+i)·3 |
| 49 |  7 | (p) |
| 50 |  1+7i   5+5i   7+i |  i·(1+i)·(2−i)2   (1+i)·(2+i)·(2−i)   −i·(1+i)·(2+i)2 |
| 52 |  4+6i   6+4i |  (1+i)2·(3−2i)   −i·(1+i)2·(3+2i) |
| 53 |  2+7i   7+2i | (p)  (p) |
| 58 |  3+7i   7+3i |  (1+i)·(5+2i)   (1+i)·(5−2i) |
| 61 |  5+6i   6+5i | (p)  (p) |
| 64 |  8 |  i·(1+i)6 |
| 65 |  1+8i   4+7i   7+4i   8+i |  i·(2+i)·(3−2i)   (2+i)·(3+2i)   i·(2−i)·(3−2i)   (2−i)·(3+2i) |
| 68 |  2+8i   8+2i |  (1+i)2·(4−i)   −i·(1+i)2·(4+i) |
| 72 |  6+6i |  −i·(1+i)3·3 |
| 73 |  3+8i   8+3i | (p)  (p) |
| 74 |  5+7i   7+5i |  (1+i)·(6+i)   (1+i)·(6−i) |
| 80 |  4+8i   8+4i |  −i·(1+i)4·(2−i)   −(1+i)4·(2+i) |
| 81 |  9 |  32 |
| 82 |  1+9i   9+i |  (1+i)·(5+4i)   (1+i)·(5−4i) |
| 85 |  2+9i   6+7i   7+6i   9+2i |  i·(2−i)·(4+i)   i·(2−i)·(4−i)   (2+i)·(4+i)   (2+i)·(4−i) |
| 89 |  5+8i   8+5i | (p)  (p) |
| 90 |  3+9i   9+3i |  (1+i)·(2+i)·3   (1+i)·(2−i)·3 |
| 97 |  4+9i   9+4i | (p)  (p) |
| 98 |  7+7i |  (1+i)·7 |
| 100 |  6+8i   8+6i   10 |  −i·(1+i)2·(2+i)2   (1+i)2·(2−i)2   −i·(1+i)2·(2+i)·(2−i) |
| 101 |  1+10i   10+i | (p)  (p) |
| 104 |  2+10i   10+2i |  −i·(1+i)3·(3+2i)   −i·(1+i)3·(3−2i) |
| 106 |  5+9i   9+5i |  (1+i)·(7+2i)   (1+i)·(7−2i) |
| 109 |  3+10i   10+3i | (p)  (p) |
| 113 |  7+8i   8+7i | (p)  (p) |
| 116 |  4+10i   10+4i |  (1+i)2·(5−2i)   −i·(1+i)2·(5+2i) |
| 117 |  6+9i   9+6i |  i·3·(3−2i)   3·(3+2i) |
| 121 |  11 | (p) |
| 122 |  1+11i   11+i |  (1+i)·(6+5i)   (1+i)·(6−5i) |
| 125 |  2+11i   5+10i   10+5i   11+2i |  (2+i)3   i·(2+i)·(2−i)2   (2+i)2·(2−i)   i·(2−i)3 |
| 128 |  8+8i |  i·(1+i)7 |
| 130 |  3+11i   7+9i   9+7i   11+3i |  i·(1+i)·(2−i)·(3−2i)   (1+i)·(2−i)·(3+2i)   (1+i)·(2+i)·(3−2i)   −i·(1+i)·(2+i)·(3+2i) |
| 136 |  6+10i   10+6i |  −i·(1+i)3·(4+i)   −i·(1+i)3·(4−i) |
| 137 |  4+11i   11+4i | (p)  (p) |
| 144 |  12 |  −(1+i)4·3 |
| 145 |  1+12i   8+9i   9+8i   12+i |  i·(2−i)·(5+2i)   (2+i)·(5+2i)   i·(2−i)·(5−2i)   (2+i)·(5−2i) |
| 146 |  5+11i   11+5i |  (1+i)·(8+3i)   (1+i)·(8−3i) |
| 148 |  2+12i   12+2i |  (1+i)2·(6−i)   −i·(1+i)2·(6+i) |
| 149 |  7+10i   10+7i | (p)  (p) |
| 153 |  3+12i   12+3i |  i·3·(4−i)   3·(4+i) |
| 157 |  6+11i   11+6i | (p)  (p) |
| 160 |  4+12i   12+4i |  −(1+i)5·(2+i)   −(1+i)5·(2−i) |
| 162 |  9+9i |  (1+i)·32 |
| 164 |  8+10i   10+8i |  (1+i)2·(5−4i)   −i·(1+i)2·(5+4i) |
| 169 |  5+12i   12+5i   13 |  (3+2i)2   i·(3−2i)2   (3+2i)·(3−2i) |
| 170 |  1+13i   7+11i   11+7i   13+i |  (1+i)·(2+i)·(4+i)   (1+i)·(2+i)·(4−i)   (1+i)·(2−i)·(4+i)   (1+i)·(2−i)·(4−i) |
| 173 |  2+13i   13+2i | (p)  (p) |
| 178 |  3+13i   13+3i |  (1+i)·(8+5i)   (1+i)·(8−5i) |
| 180 |  6+12i   12+6i |  (1+i)2·(2−i)·3   −i·(1+i)2·(2+i)·3 |
| 181 |  9+10i   10+9i | (p)  (p) |
| 185 |  4+13i   8+11i   11+8i   13+4i |  i·(2−i)·(6+i)   i·(2−i)·(6−i)   (2+i)·(6+i)   (2+i)·(6−i) |
| 193 |  7+12i   12+7i | (p)  (p) |
| 194 |  5+13i   13+5i |  (1+i)·(9+4i)   (1+i)·(9−4i) |
| 196 |  14 |  −i·(1+i)2·7 |
| 197 |  1+14i   14+i | (p)  (p) |
| 200 |  2+14i   10+10i   14+2i |  (1+i)3·(2−i)2   −i·(1+i)3·(2+i)·(2−i)   −(1+i)3·(2+i)2 |
| 202 |  9+11i   11+9i |  (1+i)·(10+i)   (1+i)·(10−i) |
| 205 |  3+14i   6+13i   13+6i   14+3i |  i·(2+i)·(5−4i)   (2+i)·(5+4i)   i·(2−i)·(5−4i)   (2−i)·(5+4i) |
| 208 |  8+12i   12+8i |  −i·(1+i)4·(3−2i)   −(1+i)4·(3+2i) |
| 212 |  4+14i   14+4i |  (1+i)2·(7−2i)   −i·(1+i)2·(7+2i) |
| 218 |  7+13i   13+7i |  (1+i)·(10+3i)   (1+i)·(10−3i) |
| 221 |  5+14i   10+11i   11+10i   14+5i |  i·(3−2i)·(4+i)   (3+2i)·(4+i)   i·(3−2i)·(4−i)   (3+2i)·(4−i) |
| 225 |  9+12i   12+9i   15 |  (2+i)2·3   i·(2−i)2·3   (2+i)·(2−i)·3 |
| 226 |  1+15i   15+i |  (1+i)·(8+7i)   (1+i)·(8−7i) |
| 229 |  2+15i   15+2i | (p)  (p) |
| 232 |  6+14i   14+6i |  −i·(1+i)3·(5+2i)   −i·(1+i)3·(5−2i) |
| 233 |  8+13i   13+8i | (p)  (p) |
| 234 |  3+15i   15+3i |  (1+i)·3·(3+2i)   (1+i)·3·(3−2i) |
| 241 |  4+15i   15+4i | (p)  (p) |
| 242 |  11+11i |  (1+i)·11 |
| 244 |  10+12i   12+10i |  (1+i)2·(6−5i)   −i·(1+i)2·(6+5i) |
| 245 |  7+14i   14+7i |  i·(2−i)·7   (2+i)·7 |
| 250 |  5+15i   9+13i   13+9i   15+5i |  (1+i)·(2+i)2·(2−i)   i·(1+i)·(2−i)3   −i·(1+i)·(2+i)3   (1+i)·(2+i)·(2−i)2 |
| المعيار | العدد الصحيح | العوامل |
| --- | --- | --- |
| 256 |  16 |  (1+i)8 |
| 257 |  1+16i   16+i | (p)  (p) |
| 260 |  2+16i   8+14i   14+8i   16+2i |  (1+i)2·(2+i)·(3−2i)   −i·(1+i)2·(2+i)·(3+2i)   (1+i)2·(2−i)·(3−2i)   −i·(1+i)2·(2−i)·(3+2i) |
| 261 |  6+15i   15+6i |  i·3·(5−2i)   3·(5+2i) |
| 265 |  3+16i   11+12i   12+11i   16+3i |  i·(2−i)·(7+2i)   i·(2−i)·(7−2i)   (2+i)·(7+2i)   (2+i)·(7−2i) |
| 269 |  10+13i   13+10i | (p)  (p) |
| 272 |  4+16i   16+4i |  −i·(1+i)4·(4−i)   −(1+i)4·(4+i) |
| 274 |  7+15i   15+7i |  (1+i)·(11+4i)   (1+i)·(11−4i) |
| 277 |  9+14i   14+9i | (p)  (p) |
| 281 |  5+16i   16+5i | (p)  (p) |
| 288 |  12+12i |  −(1+i)5·3 |
| 289 |  8+15i   15+8i   17 |  i·(4−i)2   (4+i)2   (4+i)·(4−i) |
| 290 |  1+17i   11+13i   13+11i   17+i |  i·(1+i)·(2−i)·(5−2i)   (1+i)·(2+i)·(5−2i)   (1+i)·(2−i)·(5+2i)   −i·(1+i)·(2+i)·(5+2i) |
| 292 |  6+16i   16+6i |  (1+i)2·(8−3i)   −i·(1+i)2·(8+3i) |
| 293 |  2+17i   17+2i | (p)  (p) |
| 296 |  10+14i   14+10i |  −i·(1+i)3·(6+i)   −i·(1+i)3·(6−i) |
| 298 |  3+17i   17+3i |  (1+i)·(10+7i)   (1+i)·(10−7i) |
| 305 |  4+17i   7+16i   16+7i   17+4i |  i·(2+i)·(6−5i)   (2+i)·(6+5i)   i·(2−i)·(6−5i)   (2−i)·(6+5i) |
| 306 |  9+15i   15+9i |  (1+i)·3·(4+i)   (1+i)·3·(4−i) |
| 313 |  12+13i   13+12i | (p)  (p) |
| 314 |  5+17i   17+5i |  (1+i)·(11+6i)   (1+i)·(11−6i) |
| 317 |  11+14i   14+11i | (p)  (p) |
| 320 |  8+16i   16+8i |  −(1+i)6·(2−i)   i·(1+i)6·(2+i) |
| 324 |  18 |  −i·(1+i)2·32 |
| 325 |  1+18i   6+17i   10+15i   15+10i   17+6i   18+i |  (2+i)2·(3+2i)   i·(2−i)2·(3+2i)   i·(2+i)·(2−i)·(3−2i)   (2+i)·(2−i)·(3+2i)   (2+i)2·(3−2i)   i·(2−i)2·(3−2i) |
| 328 |  2+18i   18+2i |  −i·(1+i)3·(5+4i)   −i·(1+i)3·(5−4i) |
| 333 |  3+18i   18+3i |  i·3·(6−i)   3·(6+i) |
| 337 |  9+16i   16+9i | (p)  (p) |
| 338 |  7+17i   13+13i   17+7i |  i·(1+i)·(3−2i)2   (1+i)·(3+2i)·(3−2i)   −i·(1+i)·(3+2i)2 |
| 340 |  4+18i   12+14i   14+12i   18+4i |  (1+i)2·(2−i)·(4+i)   (1+i)2·(2−i)·(4−i)   −i·(1+i)2·(2+i)·(4+i)   −i·(1+i)2·(2+i)·(4−i) |
| 346 |  11+15i   15+11i |  (1+i)·(13+2i)   (1+i)·(13−2i) |
| 349 |  5+18i   18+5i | (p)  (p) |
| 353 |  8+17i   17+8i | (p)  (p) |
| 356 |  10+16i   16+10i |  (1+i)2·(8−5i)   −i·(1+i)2·(8+5i) |
| 360 |  6+18i   18+6i |  −i·(1+i)3·(2+i)·3   −i·(1+i)3·(2−i)·3 |
| 361 |  19 | (p) |
| 362 |  1+19i   19+i |  (1+i)·(10+9i)   (1+i)·(10−9i) |
| 365 |  2+19i   13+14i   14+13i   19+2i |  i·(2−i)·(8+3i)   (2+i)·(8+3i)   i·(2−i)·(8−3i)   (2+i)·(8−3i) |
| 369 |  12+15i   15+12i |  i·3·(5−4i)   3·(5+4i) |
| 370 |  3+19i   9+17i   17+9i   19+3i |  (1+i)·(2+i)·(6+i)   (1+i)·(2+i)·(6−i)   (1+i)·(2−i)·(6+i)   (1+i)·(2−i)·(6−i) |
| 373 |  7+18i   18+7i | (p)  (p) |
| 377 |  4+19i   11+16i   16+11i   19+4i |  i·(3−2i)·(5+2i)   (3+2i)·(5+2i)   i·(3−2i)·(5−2i)   (3+2i)·(5−2i) |
| 386 |  5+19i   19+5i |  (1+i)·(12+7i)   (1+i)·(12−7i) |
| 388 |  8+18i   18+8i |  (1+i)2·(9−4i)   −i·(1+i)2·(9+4i) |
| 389 |  10+17i   17+10i | (p)  (p) |
| 392 |  14+14i |  −i·(1+i)3·7 |
| 394 |  13+15i   15+13i |  (1+i)·(14+i)   (1+i)·(14−i) |
| 397 |  6+19i   19+6i | (p)  (p) |
| 400 |  12+16i   16+12i   20 |  −(1+i)4·(2+i)2   −i·(1+i)4·(2−i)2   −(1+i)4·(2+i)·(2−i) |
| 401 |  1+20i   20+i | (p)  (p) |
| 404 |  2+20i   20+2i |  (1+i)2·(10−i)   −i·(1+i)2·(10+i) |
| 405 |  9+18i   18+9i |  i·(2−i)·32   (2+i)·32 |
| 409 |  3+20i   20+3i | (p)  (p) |
| 410 |  7+19i   11+17i   17+11i   19+7i |  i·(1+i)·(2−i)·(5−4i)   (1+i)·(2−i)·(5+4i)   (1+i)·(2+i)·(5−4i)   −i·(1+i)·(2+i)·(5+4i) |
| 416 |  4+20i   20+4i |  −(1+i)5·(3+2i)   −(1+i)5·(3−2i) |
| 421 |  14+15i   15+14i | (p)  (p) |
| 424 |  10+18i   18+10i |  −i·(1+i)3·(7+2i)   −i·(1+i)3·(7−2i) |
| 425 |  5+20i   8+19i   13+16i   16+13i   19+8i   20+5i |  i·(2+i)·(2−i)·(4−i)   (2+i)2·(4+i)   i·(2−i)2·(4+i)   (2+i)2·(4−i)   i·(2−i)2·(4−i)   (2+i)·(2−i)·(4+i) |
| 433 |  12+17i   17+12i | (p)  (p) |
| 436 |  6+20i   20+6i |  (1+i)2·(10−3i)   −i·(1+i)2·(10+3i) |
| 441 |  21 |  3·7 |
| 442 |  1+21i   9+19i   19+9i   21+i |  i·(1+i)·(3−2i)·(4−i)   (1+i)·(3+2i)·(4−i)   (1+i)·(3−2i)·(4+i)   −i·(1+i)·(3+2i)·(4+i) |
| 445 |  2+21i   11+18i   18+11i   21+2i |  i·(2+i)·(8−5i)   (2+i)·(8+5i)   i·(2−i)·(8−5i)   (2−i)·(8+5i) |
| 449 |  7+20i   20+7i | (p)  (p) |
| 450 |  3+21i   15+15i   21+3i |  i·(1+i)·(2−i)2·3   (1+i)·(2+i)·(2−i)·3   −i·(1+i)·(2+i)2·3 |
| 452 |  14+16i   16+14i |  (1+i)2·(8−7i)   −i·(1+i)2·(8+7i) |
| 457 |  4+21i   21+4i | (p)  (p) |
| 458 |  13+17i   17+13i |  (1+i)·(15+2i)   (1+i)·(15−2i) |
| 461 |  10+19i   19+10i | (p)  (p) |
| 464 |  8+20i   20+8i |  −i·(1+i)4·(5−2i)   −(1+i)4·(5+2i) |
| 466 |  5+21i   21+5i |  (1+i)·(13+8i)   (1+i)·(13−8i) |
| 468 |  12+18i   18+12i |  (1+i)2·3·(3−2i)   −i·(1+i)2·3·(3+2i) |
| 477 |  6+21i   21+6i |  i·3·(7−2i)   3·(7+2i) |
| 481 |  9+20i   15+16i   16+15i   20+9i |  i·(3−2i)·(6+i)   i·(3−2i)·(6−i)   (3+2i)·(6+i)   (3+2i)·(6−i) |
| 482 |  11+19i   19+11i |  (1+i)·(15+4i)   (1+i)·(15−4i) |
| 484 |  22 |  −i·(1+i)2·11 |
| 485 |  1+22i   14+17i   17+14i   22+i |  i·(2−i)·(9+4i)   (2+i)·(9+4i)   i·(2−i)·(9−4i)   (2+i)·(9−4i) |
| 488 |  2+22i   22+2i |  −i·(1+i)3·(6+5i)   −i·(1+i)3·(6−5i) |
| 490 |  7+21i   21+7i |  (1+i)·(2+i)·7   (1+i)·(2−i)·7 |
| 493 |  3+22i   13+18i   18+13i   22+3i |  i·(4+i)·(5−2i)   i·(4−i)·(5−2i)   (4+i)·(5+2i)   (4−i)·(5+2i) |
| 500 |  4+22i   10+20i   20+10i   22+4i |  −i·(1+i)2·(2+i)3   (1+i)2·(2+i)·(2−i)2   −i·(1+i)2·(2+i)2·(2−i)   (1+i)2·(2−i)3 |