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Olympiad workbook
Exam
Olympiad workbook
Subject
IOQM
Chapter
Permutation and Combination

Olympiad workbook · IOQM · Permutation and Combination

How many two digit numbers have exactly 4 positive factors? (Here 1...

How many two digit numbers have exactly 4 positive factors? (Here 1 and the number nn are also considered as factors of nn.)

Correct answer

30

Step-by-step solution

Two digit numbers with 4 positive factors are either the product of two prime numbers or perfect cubes. i.e. 2⋅5,2⋅72 \cdot 5,2 \cdot 7, ____\_\_\_\_ 2.47 3.5, 3.7, 3.11, ____\_\_\_\_ 3.31 5.7, 5.11, 5.13, ____\_\_\_\_ 5.19 7.11, 7.13; and 333^3 Total numbers =30=30
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