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How many numbers between 1 and 1,000 have exactly 3 prime factors, not necessarily disrinct{such as 3^3, 2^2 x 5, 2 x 3 x 5........etc, are perfectly valid)? Any help would be appreciated. Thank you.

 Jun 7, 2019

Best Answer 

 #1
avatar+23862 
+2

How many numbers between 1 and 1,000 have exactly 3 prime factors, not necessarily distinct

{such as 3^3, 2^2 x 5, 2 x 3 x 5........etc, are perfectly valid)?

 

I assume: 246

1.) 8 3
2.) 12 3
3.) 18 3
20 3
27 3
28 3
30 3
42 3
44 3
45 3
50 3
52 3
63 3
66 3
68 3
70 3
75 3
76 3
78 3
92 3
98 3
99 3
102 3
105 3
110 3
114 3
116 3
117 3
124 3
125 3
130 3
138 3
147 3
148 3
153 3
154 3
164 3
165 3
170 3
171 3
172 3
174 3
175 3
182 3
186 3
188 3
190 3
195 3
207 3
212 3
222 3
230 3
231 3
236 3
238 3
242 3
244 3
245 3
246 3
255 3
258 3
261 3
266 3
268 3
273 3
275 3
279 3
282 3
284 3
285 3
286 3
290 3
292 3
310 3
316 3
318 3
322 3
325 3
332 3
333 3
338 3
343 3
345 3
354 3
356 3
357 3
363 3
366 3
369 3
370 3
374 3
385 3
387 3
388 3
399 3
402 3
404 3
406 3
410 3
412 3
418 3
423 3
425 3
426 3
428 3
429 3
430 3
434 3
435 3
436 3
438 3
442 3
452 3
455 3
465 3
470 3
474 3
475 3
477 3
483 3
494 3
498 3
506 3
507 3
508 3
518 3
524 3
530 3
531 3
534 3
539 3
548 3
549 3
555 3
556 3
561 3
574 3
575 3
578 3
582 3
590 3
595 3
596 3
598 3
602 3
603 3
604 3
605 3
606 3
609 3
610 3
615 3
618 3
627 3
628 3
637 3
638 3
639 3
642 3
645 3
646 3
651 3
652 3
654 3
657 3
658 3
663 3
665 3
668 3
670 3
678 3
682 3
692 3
705 3
710 3
711 3
715 3
722 3
724 3
725 3
730 3
741 3
742 3
747 3
754 3
759 3
762 3
764 3
772 3
775 3
777 3
782 3
786 3
788 3
790 3
795 3
796 3
801 3
805 3
806 3
814 3
822 3
826 3
830 3
833 3
834 3
844 3
845 3
847 3
854 3
861 3
867 3
873 3
874 3
885 3
890 3
892 3
894 3
897 3
902 3
903 3
906 3
908 3
909 3
915 3
916 3
925 3
927 3
931 3
932 3
935 3
938 3
942 3
946 3
956 3
957 3
962 3
963 3
964 3
969 3
970 3
978 3
981 3
986 3
245.) 987 3
246.) 994 3

 

laugh

 Jun 7, 2019
 #1
avatar+23862 
+2
Best Answer

How many numbers between 1 and 1,000 have exactly 3 prime factors, not necessarily distinct

{such as 3^3, 2^2 x 5, 2 x 3 x 5........etc, are perfectly valid)?

 

I assume: 246

1.) 8 3
2.) 12 3
3.) 18 3
20 3
27 3
28 3
30 3
42 3
44 3
45 3
50 3
52 3
63 3
66 3
68 3
70 3
75 3
76 3
78 3
92 3
98 3
99 3
102 3
105 3
110 3
114 3
116 3
117 3
124 3
125 3
130 3
138 3
147 3
148 3
153 3
154 3
164 3
165 3
170 3
171 3
172 3
174 3
175 3
182 3
186 3
188 3
190 3
195 3
207 3
212 3
222 3
230 3
231 3
236 3
238 3
242 3
244 3
245 3
246 3
255 3
258 3
261 3
266 3
268 3
273 3
275 3
279 3
282 3
284 3
285 3
286 3
290 3
292 3
310 3
316 3
318 3
322 3
325 3
332 3
333 3
338 3
343 3
345 3
354 3
356 3
357 3
363 3
366 3
369 3
370 3
374 3
385 3
387 3
388 3
399 3
402 3
404 3
406 3
410 3
412 3
418 3
423 3
425 3
426 3
428 3
429 3
430 3
434 3
435 3
436 3
438 3
442 3
452 3
455 3
465 3
470 3
474 3
475 3
477 3
483 3
494 3
498 3
506 3
507 3
508 3
518 3
524 3
530 3
531 3
534 3
539 3
548 3
549 3
555 3
556 3
561 3
574 3
575 3
578 3
582 3
590 3
595 3
596 3
598 3
602 3
603 3
604 3
605 3
606 3
609 3
610 3
615 3
618 3
627 3
628 3
637 3
638 3
639 3
642 3
645 3
646 3
651 3
652 3
654 3
657 3
658 3
663 3
665 3
668 3
670 3
678 3
682 3
692 3
705 3
710 3
711 3
715 3
722 3
724 3
725 3
730 3
741 3
742 3
747 3
754 3
759 3
762 3
764 3
772 3
775 3
777 3
782 3
786 3
788 3
790 3
795 3
796 3
801 3
805 3
806 3
814 3
822 3
826 3
830 3
833 3
834 3
844 3
845 3
847 3
854 3
861 3
867 3
873 3
874 3
885 3
890 3
892 3
894 3
897 3
902 3
903 3
906 3
908 3
909 3
915 3
916 3
925 3
927 3
931 3
932 3
935 3
938 3
942 3
946 3
956 3
957 3
962 3
963 3
964 3
969 3
970 3
978 3
981 3
986 3
245.) 987 3
246.) 994 3

 

laugh

heureka Jun 7, 2019
 #2
avatar
0

heureka: Bravo!

You missed just one! 716 =2  x  2  x   179

Total = 247

 Jun 7, 2019

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