Sagot :
Answer:
36
Step-by-step explanation:
Factors of 30 → 1, 2, 3, 5, 6, 10, 15, 30
Ignore the 2-digit integers.
∴ 1, 2, 3, 5, and 6 can be the digit of the 4-digit positive integers.
Now, let's form a 4-digit positive integer that has digits whose product is 30.
1 · 2 · 3 · 5 = 30
1 · 1 · 5 · 6 = 30
If we use 1, 2, 3, 5 as the digits of the 4-digit positive integer, there will be 4! = 24 4-digit positive integers that can be formed when 1, 2, 3, 5 are used as the digits of the 4-digit positive integer.
If we use 1, 1, 5, 6 as the digits of the 4-digit positive integer, there will be 4!/(4-2)! = 4!/2! = 12 4-digit positive integers that can be formed when 1, 1, 5, 6 are used as the digits of the 4-digit positive integer.
Therefore there are 24 + 12 = 36 4-digit positive integers that have digits whose product equals 30.
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