Jan is thinking of a positive integer. Her integer has exactly 16 positive factors, two of which are 12 and 15. What is Jan's number?
+23246 Jan is thinking of a positive integer. Her integer has exactly 16 positive factors, two of which are 12 and 15. What is Jan's number?
Factoring 12: 1 x 22 x 3
Factoring 15: 1 x 3 x 5
So, the number must have these factors: 22, 3, and 5.
22 x 3 x 5 = 60
60 has these factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60 -- 12 factors, not 16.
So, let's try putting in another factor of 2: 60 x 2 = 120.
120 has these factors: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120 -- 16 factors!
