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Are there any numbers having 4 factors only from 30 to 140?

 Mar 25, 2022
 #1
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+1

 

(961, 1147, 1271, 1333, 1369, 1457, 1517, 1591, 1643, 1681, 1739, 1763, 1829, 1849, 1891, 1927, 1961, 2021, 2077, 2173, 2183, 2201, 2209, 2257, 2263, 2279, 2419, 2449, 2479, 2491, 2501, 2537, 2573, 2623, 2627, 2701, 2747, 2759, 2773, 2809, 2867, 2881, 2911, 2923, 2993, 3007, 3053, 3071, 3127, 3131, 3139, 3149, 3193, 3233, 3239, 3293, 3317, 3337, 3379, 3397, 3403, 3431, 3481, 3503, 3551, 3569, 3589, 3599, 3649, 3713, 3721, 3737, 3763, 3811, 3827, 3869, 3901, 3953, 3977, 4087, 4141, 4171, 4181, 4183, 4187, 4189, 4307, 4331, 4343, 4399, 4453, 4489, 4559, 4661, 4717, 4747, 4757, 4819, 4891, 4897, 5041, 5063, 5141, 5143, 5183, 5251, 5293, 5329, 5353, 5429, 5561, 5609, 5723, 5767, 5893, 5917, 5959, 5963, 6059, 6161, 6241, 6319, 6497, 6499, 6557, 6767, 6887, 6889, 7031, 7171, 7081, 7387, 7373, 7663, 7921, 7979, 8051, 8383, 8633, 8927, 8989, 9379, 9409, 9797, 9991, 10201, 10403, 10609, 11021, 11227, 11449, 11881, 19321) - 164 such numbers,

They all fall between the numbers 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137 & 139.

 Mar 25, 2022
 #2
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+1

Not sure if you wanted "divisors" or "prime factors". Here are the lists of both and you decide which ones you want:

 

33 = (1, 3, 11, 33) > 4 (divisors)
34 = (1, 2, 17, 34) > 4 (divisors)
35 = (1, 5, 7, 35) > 4 (divisors)
38 = (1, 2, 19, 38) > 4 (divisors)
39 = (1, 3, 13, 39) > 4 (divisors)
46 = (1, 2, 23, 46) > 4 (divisors)
51 = (1, 3, 17, 51) > 4 (divisors)
55 = (1, 5, 11, 55) > 4 (divisors)
57 = (1, 3, 19, 57) > 4 (divisors)
58 = (1, 2, 29, 58) > 4 (divisors)
62 = (1, 2, 31, 62) > 4 (divisors)
65 = (1, 5, 13, 65) > 4 (divisors)
69 = (1, 3, 23, 69) > 4 (divisors)
74 = (1, 2, 37, 74) > 4 (divisors)
77 = (1, 7, 11, 77) > 4 (divisors)
82 = (1, 2, 41, 82) > 4 (divisors)
85 = (1, 5, 17, 85) > 4 (divisors)
86 = (1, 2, 43, 86) > 4 (divisors)
87 = (1, 3, 29, 87) > 4 (divisors)
91 = (1, 7, 13, 91) > 4 (divisors)
93 = (1, 3, 31, 93) > 4 (divisors)
94 = (1, 2, 47, 94) > 4 (divisors)
95 = (1, 5, 19, 95) > 4 (divisors)
106 = (1, 2, 53, 106) > 4 (divisors)
111 = (1, 3, 37, 111) > 4 (divisors)
115 = (1, 5, 23, 115) > 4 (divisors)
118 = (1, 2, 59, 118) > 4 (divisors)
119 = (1, 7, 17, 119) > 4 (divisors)
122 = (1, 2, 61, 122) > 4 (divisors)
123 = (1, 3, 41, 123) > 4 (divisors)
125 = (1, 5, 25, 125) > 4 (divisors)
129 = (1, 3, 43, 129) > 4 (divisors)
133 = (1, 7, 19, 133) > 4 (divisors)
134 = (1, 2, 67, 134) > 4 (divisors)
Total = 34 such integers

 

 

36  = 2  2  3  3 >4 (prime factors)  
40  = 2  2  2  5 >  ....................... 
54  = 2  3  3  3 >  ........................  
56  = 2  2  2  7 >  ........................  
60  = 2  2  3  5 >  ........................  
81  = 3  3  3  3 >  ........................  
84  = 2  2  3  7>  .........................  
88  = 2  2  2  11 > .......................  
90  = 2  3  3  5  >  .......................  
100  = 2  2  5  5 >  ......................  
104  = 2  2  2  13 > .....................  
126  = 2  3  3  7 > .......................  
132  = 2  2  3  11 > .....................  
135  = 3  3  3  5 >  ......................  
136  = 2  2  2  17 > .....................  
140  = 2  2  5  7 > ....................... 
Total ==16 such integers. 

 Mar 25, 2022
 #3
avatar+117857 
+1

If a number is the multiple of 2 prime numbers it will have exactly 4 factors

 

eg

 

7*11=77    factors are   1,7,11,77

 Mar 25, 2022
edited by Melody  Mar 25, 2022
 #4
avatar+117857 
+1

or maybe you meant that the factors have to be between 30 and 140 ??    [The meaning of the question is not clear]

 

1 is a factor for all integers ....  

2210269 = = 31*37*41*47 

the only other factors are 1 and 2210269

 Mar 25, 2022

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